A question will be closed whenever there are five Close votes on it, unless one of those is a moderator (in which case the question is closed immediately). It's important to note that close votes age away if no new votes are being added.
The effect of Leave Open votes is to take the question out of the review queue: if (# of Leave Open reviews) is three or ...
My checklist that I try following:
Do I understand the original question?
No? Select Skip.
Comments exist already?
Can I guide the poster to a more-correct answer?
Yes? Do so, then select Looks OK
No? Select Skip
Does the comment explain the error?
Yes? Select Looks OK.
No? Explain why it's wrong, select Looks OK.
The number of "Looks OK" votes depends on the number of flags on the post, cf. this meta.SE post:
Each review task requires a minimum number of "Looks OK" reviews (2 on SO, 1 everywhere else) to be dequeued; this number increases by one for each pending flag on the post (edits, closing and deletion dequeue the task in the normal fashion).
I feel your pain.
But, formally, "Looks OK" is the only way to go. It is an attempt to answer the question. Perhaps it's horrible, not useful, confused or whatever else, but it is a valid, if ugly, contribution. The best course of action is: Downvote it into oblivion. (then hit "Looks OK", feeling slightly guilty)
A button expressing something like "Not OK,...
It's not possible to change the flag/VTC reasons, other than the few custom reasons that appear under "off topic" (and that's only for questions). I mean, it would be technically possible, but the feature doesn't exist in the SE system. So I think we can safely conclude that adding a custom flag reason to catch non-mainstream answers won't happen.
We have ...
I think rob's answer provides some insight as to why the review queues exists, but I think the answer to the question is as simple as
"You aren't reviewing the question when you are outside the queue; when you click the "close" button from the post page, you are just voting to close the question, even when there are existing close votes."
So even though ...
Close votes can age away, at which point the voter won't be able to VTC on the same question again...
Moderators can remove questions from the queue by closing them or selecting "Leave Open". In the latter case, the outstanding close votes remain on the question until the question is closed or the votes age away (see #1).
If a certain number (currently ...
This is fixed now. You should no longer see the same post in the First Posts, Late Answers, and Low Quality review queues.
It's still possible to come across the same post in the other queues though. For example, you might see something in Suggested Edits, and then later in the Reopen queue.