What does "ALTER DATABASE ... SET NEW_BROKER" do? Is there anything to worry about?
Only if your database participates in distributed conversations. NEW_BROKER changes your service_broker_id. If you created any route with service name and service instance then it will become invalid as the route service instance value no longer reflect the destination service_broker_guid. It goes w/o saying that doing NEW_BROKER on a database that does have running conversations that span isntances (or even DBs in the same conversation), these conversations will have one half 'nuked' and the other half will be left stranded, unable to make any progress (will have to be cleaned up with END ... WITH CLEANUP or the other database will also have to be NEW_BROKER-ed).

Be aware that NEW_BROKER affects hidden conversations like the ones created by Event Notifications.

If everything you have is local, in the same db, then you have basically nothing to worry about.