This idea is not totally original: there was at least an attempt at a journal club in chat in 2011. That, in turn, was inspired by mbq's (and Cross Validated) idea, which seems to have happened at least twice. We already have users do this, so I'm really just suggesting that we more actively encourage this. So here's some ideas I have. Feel free to add ideas for the process, suggest ideas for papers.
What do you mean by a journal club?
Many physics departments have informal meetings where (mostly) graduate students meet for one or two hours with coffee, beer, and/or pizza, and discuss a recent research paper. Some departments even require their students to do this. Typically, someone will choose the paper for that week's meeting, everyone will read it before they meet and come up with questions for discussion. Then the group discusses the paper in some detail.
Why would we want to do this?
As several people have noted, and Manishearth has summarized, we've been having some difficulty recently with long-term, highly-respected users leaving or cutting back their involvement. We are also seeing a lot of homework questions that are either too basic for the regular users' tastes, or simply don't show any work at all. I hope that this idea will help fix both of those. First, by providing more interesting questions of a higher technical level, I hope that we can both retain our current users' interest and make the site more inviting for professional physicists who aren't already here. Second, this will help populate the front page with questions that aren't homework, which should help discourage students from asking for help on their homework.
So how would that work here?
Someone finds a research paper they think is interesting. They develop a question about that paper, and post it to the main site. For a theory paper, this might be about a missing step in a derivation. For an experimental paper, this might be about the experimental setup. For a computational paper, this might be about the approximations underlying the computational model. Regardless of the kind of paper, the question should otherwise be a valid, on-topic question for Physics.SE.
In addition to that, we will also invite suggestions for papers. People can add papers to this question as Answers, and others can vote those papers up or down. Other users can then use those votes as a gauge of how interested people will be to see a question about a particular paper.
Further, there will be no restriction on the number of questions that can be asked about a particular paper. After all, any good physics paper should invite several questions. Some questions will be distinct enough that they can be asked in parallel, while other questions will be generated from the answer to a previous question. We may even want to suggest a time-period (say a week) where people try to focus on one particular paper, and dissect it with many questions.
What sort of papers should I be looking for?
Any paper, past or present, that is within the scope of the site. They can be historical, current, in your sub-discipline, something you need for your research, something only of passing interest to you, whatever. The only real limitation is that it should be published in a real journal or posted on a real pre-print server. This journal club will not be a place to ask for feedback on a manuscript you are working on, and it really won't be appropriate for discussing some crank's magnum opus about the earth sitting on top of an infinite tower of turtles.
Should I worry about Open Access?
Yes and no. Not everyone here has access to many journals, so if you ask about a non-OA paper, you are excluding those who can't get a copy of that paper. That will presumably lower the quality of the response you get. On the other hand, some of the more prestigious journals hate Open Access, and many sub-disciplines of physics just haven't picked up on OA yet. So there are many papers that will produces good questions that just aren't OA papers.
Ultimately, feel free to base your voting and preference on the accessibility of a paper, but don't feel obligated to.
Should I tag such questions as journal-club, or something like that?
NO. Tag these questions as you normally would. We will compile a list of these questions here so people can find them easily. But creating a new tag for this project isn't useful; it would be a meta-tag.
Ok. This sounds great. What can I do to help?
Suggest papers here as answers. Vote on papers that you like. If you want to skip the whole suggestion-vote-ask process, just go ahead and ask a question about your paper.
This sound okay, but it would be even better if you did...
If you have suggestions for improvements, please feel free to add them, either as an answer/comment to this question, or by editing this question.