From my personal experience, the best thing that helped my stability in the snatch is to do a full snatch regardless of the weight, i.e., do a full snatch even on your warm ups or if you happen to power snatch the weight do an overhead squat and sit in the bottom position for a few seconds.
I saw Klokov once do an exercise, which I assume was for snatch stability, where he got into an overhead squat and literally hopped across the gym. A bit crazy and wouldn't recommend it but it shows that you can get creative with these things.
Never had an issue with jerk stability so can't recommend anything. However, do a search and you'll find lots of assistance exercises that improve stability.