Like everyone else, I'm not sure how much definitive advice I can provide seeing as I'm still in the middle of the process, but I can relay what various advisor-types have told me and what my experience has been.
About grades, Step II, research, recommendation letters: As stated earlier, psych probably tends to be less focused on board scores than other specialties. My school's program director told us that the dean's letter and 3rd-year clerkship evaluations matter much more than board scores (and the 3rd-year psych clerkship evaluation matters more than the 4th-year sub-I, in fact). As for grades, well, obviously being AOA helps, but it's not necessary as it would be for, say, derm. As willow212 said, you should get four recommendation letters -- no more than two from psych, at least one from something as close to medicine as possible (primary care, peds, neurology would all be good), your last one from something else of your choice (as long as it's not psych) -- a research advisor, another medicine person, someone in a less-related rotation who would have extremely positive things to say about you. In terms of research, I have to admit I'm not a research-oriented person, and I don't think I could convincingly fake an interest in a research-only career, so it wasn't even worth trying for me. I've been told that while research is nice, you shouldn't force yourself to do it if you don't want to. And you can get publications without doing research -- look into case reports and writing for student journals.
I can't really say what would help you with the most competitive programs, other than an overall solid record. I don't think there's any single thing that will sell you to a program. I do think a good performance on an away rotation can help (and it'll also give you a sense of how psychiatry is practiced outside of your medical school), but don't forget that an away rotation can just as easily hurt as it can help. Also, other schools may think you're less interested in them if you don't choose their school for your away rotation.
As for good electives....well, I've done inpatient and C/L electives. I think the inpatient rotation is important because it really gives you an intensive exposure to treating the whole person, and it condenses it into a time frame that's likely to fit within a rotation. While an outpatient elective might be more realistic, you won't see an individual as often, so you may not get as good a sense of the treatment course of any single person. Otherwise, I suppose it makes the most sense to choose other electives based on what interests you the most; I don't think your choice would matter that much for residency applications, at least.
No feedback on interviews yet, but my first interviews are coming up in the next two weeks, so you'll be sure to see me posting about program feedback.
Hope this helps, and good luck on your psych rotation!