I did. I have my DO, one science and the non-science LOR in the works. I'm waiting until next semester to get my last science LOR, I just hope I don't regret waiting until then.
I'd definitely wait. For one thing, the prof hasn't had much time to get to know you by mid-semester, so s/he won't have as much to say. Also, I think the med schools expect the recommender to comment on how you did in their class, which is impossible if it's still in progress. (Not to mention that you could theoretically have a situation where you get an LOR at mid-semester when you're doing really well in the class, and subsequently bomb the final and get a so-so grade. That would really make your recommender look bad.)
I think the only time you'd ask for an LOR before an activity is finished is for an ongoing research or volunteer job, where you've been working there for some time and the letter writer already knows you fairly well.