Uniqueness of MUIDs on the network

This link Core API - Core Documentation says: "They are guaranteed to be unique within the game and likely to be unique globally"

I save the MUID of ntworked object on the client (so as not to waste extraEvents.BroadcastToPlayer) and send an Events.BroadcastToServer to the server at the right time in order to destroy the object.

Are there any problems? I haven't identified it yet, but there weren't many tests.

Your setup should be fine.