I think most of them have been listed already, but here is my list:
1. Time and time management.
2. What society thinks of us.
3. Extra drama (each relationship adds extra complexity).
4. Having to contemplate your feelings more and work extra hard at communications (some people may see this as a positive though).
5. With more relationships, there will probably be more breakups you have to deal with. (Sort of goes with drama.)