The best approach is indeed to submit an answer that pays special and enhanced focus to the alleged error.
As a preliminary comment, I think that this question is probably a general stack exchange meta question, not a question specific to physics.meta.stackexchange.com.
As a second preliminary comment, I think option #1 needs to be split up. Option #1 says, "Answer the question as best I can, even if the answer technically does not answer the question." A problem here is "as best you can." In most cases, I think a reader would take this to mean, fix the implied errors, and just answer the intended question. Indeed, in this answer I will end up giving two examples where this occurred. But, as you've pointed out in your comment, what you actually meant is to avoid "fixing" the question (the opposite), and to focus on the issue(s) with the question instead. In this answer, I will call your intended option #1, option #1, and the fixing option, option #4.
To be extra clear, these definitions mean that only option #1 is able to encompass the contentious situation that I encountered yesterday and which the asker, Javier, also apparently encountered in which an answerer submits an answer that intentionally refuses to try to answer a potentially intended (i.e., fixed) question. However, option #1 is not restricted to this, either. My option #4 here is the least antagonistic option possible, for it glosses over potential issues and makes the asker look the most intelligent; all the other options #1-#3 are all largely critical of the question itself.
For reasons I will soon give, I think option #1 is the correct answer. #2 (closure) is just censorship and it fails to help the poster with their real roadblocks in knowledge. It is worth noting that closure, originally thought of as a great idea for these sites, was arguably the main thing the founder reversed when he left to to found Discourse. The raw point system is, itself, already a strong mechanism to prevent worthless clutter. #3 (a short comment) is horrible because it suggests that the alleged issues are trivial when they rarely are. I think #4 is the probably the most common route taken on stackexchage, and I will attempt to show why it is a bad option.
To help think about which approach is best, let us consider the ideal, perfect, learning situation. Then, let's pretend a writer here wants to get as close as possible to this idealized learning situation. Then, let's consider how to handle a bad question. Usually, these are questions which assume something that a potential answerer disagrees with.
I think it would be hard to dispute that a close-to-ideal learning situation is a tutee learning with a tutor who is knowledgeable in the subject being taught. One reason is that it is generally thought that a low student-to-teacher ratio is good, and this has about the lowest ratio that is still realistic. The question at hand, therefore, can probably be narrowed to, "How should an ideal tutor handle a tutee asking an allegedly wrong question?"
Without any doubt, in this situation the ideal tutor would not just internally correct the question and continue onward. Rather, the ideal tutor would put a spotlight on the implied alleged error of the question.
One reason is that knowledge of a subject, especially one like physics, is like a pyramid. In this analogy, learning is like building this pyramid of knowledge in a tutee's mind. A good tutor will try to make a good, strong, pyramid as efficiently as possible. The middle and upper layers of the knowledge pyramid require a good foundation of math, simpler physics, etc. Only once a solid foundation is in place should a tutor move the tutee up to the next brick level:
If, in building an upper layer, an allegedly bad brick is discovered, then all attention should be directed just to the allegedly bad brick below. Otherwise, the tutee will not have an ability to self-re-derive the layer the tutor is working on correctly. They might be able to memorize solutions to specific cases, but they will fail as soon as they are faced with an altered scenario, because this is when they will need support from that allegedly bad brick. The upper layer being built will be made of weak material, and tainted by potentially false knowledge. It will probably just fall apart in the student's mind after an arrogant tutor tricks oneself into thinking they've successfully built the upper layer and can now go even higher.
In my analogy, what such an arrogant tutor (or physicist for that matter) would really be doing is building a jenga tower:
The entire structure of knowledge will just crumble and fall apart as the student, once faced with, for example, a test question they didn't exactly see before, realizes they don't actually understand much of anything about the subject, and that, for example, they are going to get an F on the exam they are taking. The worst time for them to discover they have no real idea what is going on is during an exam!
There are a few approaches to fixing an allegedly bad brick revealed by an allegedly bad question. If it were me, I would probably say, "Wait a second. Let's back up a little. Your question was $x$. Are there any interesting assumptions you are making here? ... Can you show me how we got this?"
Perhaps you can see where I am going. I would want the student to eventually discover own their own that there is an error in their question. Alternatively, there is the possiblity that I'm wrong, in which case I will discover that I am the one making the error.
Of course, a good tutor might instead just directly point out the alleged error. Each approach will focus on the allegedly weak brick.
To continue the spotlight on the issue, I'd have the student do some problems about that "bad" brick that prove and demonstrate that the deficit in the question was fully and completely resolved. Only then would I allow the question originally asked to be addressed.
Importantly, there is the real possibility that the allegedly bad implied assumption is actually correct. (This is why I am, arguably irritatingly, insisting on injecting the "weasel word" allegedly throughout my answer.) Here we can really see why #2, #3, and #4 are horrible answers. By not directing the spotlight to the correct areas, potentially wrong assumptions can then persist in the ecosystem of potentially true and potentially false knowledge.
A good example to illustrate my position are the questions and answers here concerning understanding resistance and Ohm's Law. The situation with Ohm's Law is that a lot of engineers need to use this law. However, to derive it from first principles, getting the correct conductivity coefficients from basic things like atomic properties, could be rather complicated. I don't think it really requires quantum molecular dynamic simulations of finite temperature density functional theory, but this is the implication I gave here in response to someone claiming the law is impossible to derive theoretically.
Obviously, this would be over the head of your typical electrical engineer, so my guess is that a lot of textbooks resort to the Drude model in attempting to explain Ohm's law in which the electrons and atoms are treated like a bunch of billiard balls. The alleged benefit might be that this is easier to teach and give problems on. Within metals, due to the effects of quantum mechanics and the relatively low energies of the electrons, in my opinion the electrons should not generally be treated in this fashion. That is to say, some of the educational models being used are, essentially, not even worthless, but of negative value, getting in the way of real progress.
Perhaps you can see where I am going with this. If not, I think what is happening is that teachers are teaching bad models. This perhaps results in their students having a lot of questions. Their questions often have implied alleged errors in them, because the students are genuinely and rightfully confused. I think that the real problem is probably that the teachers are not teaching physics accurately. This trickles down into confusion in the students, who come here, hoping to resolve their problem. Some of the poorly instructed students end up here, thus exacerbating the situation.
I am arguing that the worst thing possible is that the accepted answers pertaining to issues with the Drude model are glossed over here (the #4 approach). Stackexchange then just worsens the underlying problems here, arrogantly suggesting the issues a student is having is their fault instead of the teacher's. It would foster people thinking they know what is going on when they really don't, perpetuating bogus physics and disinformation, stifling creativity and progress. That is not ideal for stackexchange.
Consider the currently-accepted answer to "Can someone in a simple way explain [to] me what the Fermi level is and what [it has] to do with conductivity[?] My teacher said that Cu conducts electric current better than Al because of something in relation to [the] Fermi level[.] I didn't get him very well, so please explain [to] me what it is all about, but in a simple way." I think that the currently-accepted answer has serious problems, largely because what is probably the best answer, involving Kubo's formalism, is complex and not that simple.
This example underscores the dangers of glossing over issues in questions. Doing that allows people to think they understand how something like conductivity works, when they probably don't.
This is not some bizarre example, either. Can you estimate the fraction of physics papers that convert into Nobel prizes? A hint is that there is only one prize award per year, but the number of papers published each year is growing rapidly. Most papers are loaded with what history will prove to be bad, implied, and ignored assumptions. This is largely because people want to be nice and to not criticize, something that isn't always ideal. They gloss over these more important questions, such as the assumptions being made, allowing a train of false knowledge to pollute and weaken the knowledge pyramid. I think that the progress of correct physics would be greatly increased if people were willing to question their assumptions in a free and direct fashion. This requires putting the spotlight onto the truly important issues. Here, that requires a separate answer largely focusing on that.
This is especially true because the implied assumptions of a question that an answerer thinks are wrong might actually be legitimate. In other words, the answerer might be wrong. Sometimes, an outsider or a bright eyed, bushy tailed wondering student is the first person to discover that an entire branch of alleged knowledge is actually wrong, and needs a full rework.
Consider the arguably simple question about how much work is required to raise the temperature of water some amount. You probably are thinking this is about the dumbest, simplest question one could ever ask. I attempted to answer it here. However, I soon changed my answer, and concluded that my original answer was wrong. It turns out that the questioner was probably asking the question because they didn't think the energy got converted into heat. So, the issue where I thought the asker was wrong about, and the #4 approach as defined by question (which says we should just gloss over this), was probably the dispositive, deciding aspect of it; the part of the question that I thought was wrong, I now think was actually mostly right. By comparison, the non-accepted answer does #4; it glosses over the issue, and blindly assumes all energy is converted into heat, which I now think (like the questioner) is wrong. This illustrates how the #4 approach is probably bad--it can lead to bad physics.
How can one ever allow an important discovery to be made if it is hushed up by an arrogant comment or by conclusary reasoning?
Indeed, by reverse logic, if one wanted to impede the progress of awareness of reality, or what was going on, one would intentionally ignore key issues with questions and use conclusory arguments. At the risk of committing the felony here of using an example from outside of physics, have you ever wondered why a lot of politicians often morph questions away from the literal topic and onto another with a phrase like, "The real question is..." This is exactly #4.
Focusing on arguably trivial issues of a question allows for a stronger knowledge pyramid in a tutee's mind. It requires being somewhat irritating, pedantic, and taking a more literal approach in which all parts of the actual question are taken seriously. Keeping within Ohm's Law, a good example of what I mean here to this "literal" approach to answering questions (i.e., not quietly fixing them) is my answer complimenting Thomas' answer here. (I think Thomas glossed over the Maxwell's equations restriction in the answer.) I think that glossing over issues (like this) can create ambiguity in the questioner's mind about the real answer to their real question. Most good students will get hung up on that issue. The teacher will plow onward, but the student won't take it in, and it will be a waste of time. Allowing such ambiguity is building a weak pyramid of knowledge, and against the goals of stackexchange.
In summary, not only because it is in the best interest to the questioner, but also because it is in the best interest to the field of physics, the best approach to an allegedly bad question is probably to have a tutee focus on the alleged issue.
Converting from the tutor-tutee scenario I have invoked to the web-based system here on this site, I think this entails writing a full-fledged answer (option #1) that brings focus to any alleged issues in a question, not in an x-character comment (#3).
