One large class of problems I'm thinking of is simply outside the scope of CRDTs. The whole idea of _eventual_ consistency doesn't really work for things like payment systems or booking systems. A lot of OLTP applications have to be consistent at all times (hence the O). Money must not be double spent. Rooms or seats must not be double booked.
The other class of problems is more debatable. CRDTs can guarantee that collaborative text editing results in the same sequence of letters on all nodes. They cannot guarantee that this sequence makes sense. Authors can step on each other's toes.
Whether or not this is a problem depends on the specific workflow and I think it could be mitigated by choosing better units of storage/work (such as paragraphs rather than letters).