To a certain extent, it depends on the schools and how competitive your application is, but in general, no... Everything is fine.
A lot of people's letters turn up late. There is still plenty of time before secondaries and letters have to be complete at most schools.
If your application isn't too strong, though, you'll be heading to waitlists if you don't get it sorted in the next month or so. If you've got a good application, you'll be fine, though.
Remember, schools are still slightly geared towards being able to accept people who took the August MCAT in past years (when there were only two dates - April & August) and it took time for the results to come back after that. So they fully expect to have applications coming in for a long time.
