Cannot think of any problems. Obviously the database dump should be created while your node is down, and the new node should be down too, while you are copying the database.
The database might contain stale (unreferenced) transactions which would not get synced when you did not use a database, but those should not hurt either (if you have the disk space).
Consensus is currently fully controlled by the coordinator, so even if 50%+1 nodes would copy your database, it would not affect consensus (and even if there were no coordinator, it would only affect consensus if all the nodes would copy and use your database at the exact same time).
Obviously, you should not use a database snapshot that is older than the last (public) IOTA network snapshot.