Anyway, I got it back with lots of corrections and then started to wonder am I supposed to be doing more editing before sending it in??
Ideally, instructors would like you to correct all the things you know how to correct, so that what the instructor is commenting on are things you actually don't know how to do or struggle with getting correct. I don't know how many revisions any one person needs to get to that point -- but that's the ideal. That way, the instructor's time is spent on correcting things you really don't understand, or have missed despite revision efforts. For example, I know that you're is the contraction of "you are" but I typo it all the time...and then I read what it SHOULD say instead of what it DOES say...and my critique group pointed that out until it finally got through my head that I need to do a search for "your" in every manuscript to make sure I fix it. That's the kind of thing your instructor might do -- point out those "blind" errors for you so that you can build a step in to search and fix them.
But things you really could do and know how to do -- those you should do if possible. Don't let that paralyze you toward sending the assignment off...but if you have the time and you know how to correct the mistakes, that'll allow the instructor to use his/her time on instructing.