I don't really know if these bugs are co-op exclusive or not, but here we go:
1. "Kill X" optional missions tend to not register even if you kill that boss target, thus we get stuck on the map and forced to restart it, wasting 1 day for nothing.
2. Tarkus sometimes completely freezes while trying to throw grenade and wouldn't be able to move until being incapacitated. Strange thing is while host played him a fair amount of times, he didn't encounter this problem not even once, while under my command it can trigger twice on one map.