below a list of (more or less motivated) possible improvements.
As a starting tautology, if you want more research-inspired question, attract more researchers ! When I read some of you claiming they want pure theoretical discussion, I'm horrified. Physics is a science, and science means models AND experiments. Could be really fine to discuss more about experiments. I don't know how to do that, but restraining to pure theory of course restrain to less than the half of the physics community ! Note that attracting more experimental discussion may oblige experimentalist to discuss about their setups, and may resolve a lot of problem associated with this main-stream envy to publish only Science and Nature papers which usually do not contain enough materials for an experiment to be reproducible.
PS: The next two paragraphs have been edited, after discussions with Dilaton who pointed their excessive (even insulting) character that I apologize for.
I've the feeling that some of the answers are not at the level of the questions. It seems to me -- especially in the field of QFT that I don't know well but I'm trying to learn more -- that the answers are sometimes too technical. I'm a condensed matter physicist interested in quantum field theory, and most of the time the answer I read about QFT sounds inconclusive and of pure semantic polemics. The questions I read in quantum information and condensed matter topic (topics that I know better indeed), looks for me much more friendly and pedagogical. Still the level of the question is not amazingly high in average. Maybe a good point to have better question is first to have better answer.
Still regarding the different topics related to different communities: I've the feeling that the level of the questions crucially depends on the topic. For instance (and this might well be once again because I'm poorly knwoledged in QFT) it sounds for me that some post in condensed matter are really good, instructive and well documented. In few words, the condensed matter topic might well be still preserved from the deseases mentionned in the above question. The question still remains on how to get higher standard of course.
Maybe the modo should be a little bit less stringent regarding the rules at the beginning of a new question (examples: "you should add this in your answer, not as a post", "this is not a new answer, this is a comment of the previous one", "this is not a new question" ..., which sounds time consuming for them and not really helpful I believe). A perfect (and pedagogical) method for me would be to let people answering the way they want at the beginning (in post, answer, comment or whatever, just sending a reference or starting calculating from scratch, stopping a calculation, coming back latter for improvement, etc... well in a messy way, as almost all physicist desks are, isn't it ?). When the author of the question understands the point, HE / SHE writes HIMSELF / HERSELF the answer. It obliges to 1) know better how the site works technically (i.e. how long and boring it is to write on a small 10-lines box a long answer :-), 2) be responsible for getting the answer, 3) improve the presentation and pedagogy of the site, since the author's answer can be displayed at the beginning of all the answer. Also, this method helps in cleaning the post. Of course it is not perfect.
I'm not sure I understand what you want. Do you want open problem question ? Sure, I can do that. It will take me an entire afternoon each time to write correct presentation of the problem(s), to type all the maths and correct them. But sure I can do that ! Will result long unanswered posts for sure. Is that what you want ?
I prefer for myself discuss with colleagues around me first, then discuss with friends in conferences, then think hard for years before saying I can not resolve a problem. I will always use this web-site for question that I know some of you can answer better than what I found so far in non-specific literature, to clarify a specific point, ... well, I'm using Physics.SE for pedagogical reason, to discover a new subject for instance.