Always ask permission for taking photographs of people, especially the Masai;
be prepared to offer money or some item in exchange.
It's illegal to take photos of bridges, harbors, military installations, railway stations, airports, etc.
Don't travel to the islands by dhow (local sailing boats). Except for organized tourist trips from Stone Town in Zanzibar, it is illegal for foreigners to travel by dhow from mainland Tanzania to any of the islands.
Bargaining in markets and shops is accepted and often expected from the client.