It is worse than GMail. It tends to come in waves, there can be weeks where I barely get any spam in my inbox and then there is sometimes a couple of messages per day. I guess marking spam (Fastmail also uses a naive-bayes-based filter) and/or servers being added to a blacklist stops those waves.

I don't recall the opposite (false positives) ever happening.

I would say the numbers are generally small enough that it does not bother me.