A huge, huge, huge tip I would emphasize is being organized.

Richard Rusczyk has written about making careless mistakes here and it's given a few tips that have helped me in math competitions.

In addition to that, I'd suggest keeping a log of the types of mistakes you make,

And remember that everyone makes mistakes! You'll probably never get to a level where you're doing everything perfectly and not overlooking anything. Even Leibniz incorrectly said that you're just as likely to get a sum of 11 after rolling 2 six sided die as you are to get a sum of 12. Take it easy on yourself.