You know, the process really is not random at all. Everyone says that it is for some reason, but it really really is not.
This does not go for someone with 6 interview invites and no acceptances yet, because you might just need to wait, but if you interview 6, 5 or even 4 places and get flat out rejected from all of them then you were doing something wrong at your interviews. There was a way that you were interacting with the interviewers (or other interviewees at a group interviewing school) that made them unable to see you as a doctor, plain and simple.
Listing accomplishments at an interview is not important. They know all of your accomplishments already! If they ask you to name one or ask you a specific question about one, obviously answer it, but just have a normal human conversation for goodness sake. Succeeding at a med school interview is like succeeding at any other social interaction: what you say is not nearly as important as how you say it. Being confident and totally at ease with yourself, and being able to read other people well enough to know whether you are putting them at ease is most important.
I find that most of the people I'm applying with that I talk to who "failed" at their interview after feeling like "they did so well" and think "this process is so random" actually mean that they shoehorned every possible sales pitch they could into their interview without stepping back to consider that the interview is more about being (or acting like if you are still working on your self-esteem) a confident, happy professional than "proving" that you have the potential and credentials to someday be one.