Applying to residency was a totally different experience for me. Before I began the process, people told me that residency interviews are as much (or more) about the program selling themselves to you than you selling yourself to the program. Obviously, this is specialty and program dependent, but the residency interview process is much better than the med school interview process. Remember, only 1/3 of people applying to med school get in, whereas for residency most specialties have closer to a 1:1 ration of spots:applicants. Even the most competitive specialties have about an 80% match rate for US seniors.
As far as the strength of your application, I feel that the most important factors are LOR, third year grades, and step I scores. I was told the Dean's Letter is important to some, but this is merely a reflection of your grades and evaluations. AOA is also important for some, but again this is usually a reflection of your grades. These can get you the interview, then you just have to be personable. Other things like research experience, volunteering, student government, involvement in national organizations (AMA, AMSA, etc) can also help.
Hope this helps and try not to stress out too much.