Thanks for all the feedback!
1. Hmm, perhaps we could change the game model? Instead of solving as many as you can in three minutes, we could (1) have a set time per problem, and a fixed number of problems or (2) have some system to add back time for correct answers.
2. This is on our todo list!
3. Yes, see my comment from above -- we're thinking of simple ways to accept slight variations. A way to contest variations might is a good idea.
4. How do you propose we do this?
5. So right now, a problem is worth ceiling(length of our solution / 10.0) points. This seemed like a good way to reward harder questions proportional to the time spent solving them. Any other suggestions?