When you file AMCAS, you can put down courses you are currently taking or will be taking in the future. So, even if your BCPM GPA is a bit lower than you'd like, they'll see that you are trying to make ammends. Also, one bad calc grade won't bring the BCPM GPA down that much when it's combined with all of the science courses.
I filed my AMCAS at the end of June. I had taken the April MCAT, and I had some time off between the end of school and starting my summer job, so I worked on it then. It could have been submitted starting around June 11, but I didn't want to be one of the first people to submit, considering last year's technical problems, so I waited about two weeks.
Advantages to early AMCAS filing:
I didn't want to have to do secondaries during the school year when I would have homework and other responsibilities. Yeah, it sucked doing them during the summer, but it was such a huge weight off my back to get them done before going back to school.
Looks good to the schools. Many interviewers commented that they like students doing things orderly and early.
Early interviews. Good for rolling schools. At some of my interviews, there were EDP applicants interviewing on the same day. Also good for non-rolling schools, since it looks responsible. Also, early interviews mean early acceptances. So if a school you like lets you know in October, you may be able to cancel some November and December interviews, and save a good deal of $$$$. Since you start interviewing earlier, you see what it's like, and by November, you'll be a lot less nervous, and may appear a lot more confident then someone who has never interviewed before.
You application may be looked at several times. For many schools, they go through applications in rounds, and each time select a certain number to interview (or accept). If your file is in early, it will go through more of these rounds.
Since your interview invites will come in earlier, you will have a bigger selection at open dates at some schools, making scheduling a lot easier, and often cheaper as well.
Good luck! I'm sure everyone here will do well.