I had the same problem last cycle. Borderline applicant, I got everything in but committee letter wasn't in until August 28th, and then it took weeks for some schools to mark my application as complete. Last cycle did not go well for me (reapplying now) but I don't blame the letter timing 100% because I am a weak applicant to begin with.
However, someone else at my school got into only his state school and he had a 40 MCAT, a 3.97 GPA, significant research and community service experience, significant shadowing experience, and was involved in interesting extracurriculars throughout college. He applied to 25 schools, got 3 interviews, and 1 acceptance. I think the committee letter timing had something to do with it.
I am not trying to scare you, I am just still bitter about the whole process (our school is very pompous "don't contact us and ask when letters will be in", "the deadlines don't apply to us", etc).
Just keep on top of everything. Once AMCAS gets your letters make sure you are tracking all your schools and that they have received them.