Be considerate when you think about taking pictures of people. Especially in more rural areas. People don't like it when you take pictures of them so make sure to ask in advance. Otherwise you might end up being chased by angry Tanzanians! I'm not kidding. A friend of mine practically had to run for her life after having taken some pictures at a market in Mwanza. If you insist on doing it, bring someone local who can sort out any misunderstandings or bring another mzungo and make him/her pretend to be posing in front of the camera. The reason people don't like having their picture taken is different according to region. Some places they claim the camera is connected with witchcraft and steals their soul. Others again simply don't like it because they have found themselves on pictures being used in papers or magazines.
Greetings are very important in Tanzania - not least in Mwanza region where the Sukuma have all sorts of greetings for every occasion. If you greet someone older than you, you should always use a 'shikamu' which means something like 'I hold your feet'. It is a way of showing yor respect and it is always a good idea to say it to any one older or important. The correct answer should be 'marahaba', so practise this also, as children might say shikamu to you, and it would be considered very rude not to give back the right reply.
Other greetings are 'habari' or 'salama', which are all replied with 'nzuri'. Some times you will hear younger people saying 'mambo' or 'jambo' to which you can answer nzuri or salama but also 'poa', 'safi sana/kabiza' or 'freshi'. But never say that to an older person.
Also it is rude if you don't reply to these greetings with a correct answer. A simple nod with the head won't do, so do yourself a favour and learn a couple of these greetings.
It seems obvious, and you probably know already, but don't wear clothes that are too exposing. Tanzania is a country with a lot of Muslims and a lot of muslims live in Mwanza. Furthermore, christian tanzanians also disregard this kind of clothing. There are not many tourists or wazungo in Mwanza, but the people here ARE used to the western kind of style, and as opposed to the villages og more rural areas, you CAN walk around in sleeveless t-shirts showing your stomach and shorter skirts or shorts. People will stare at you, however, and it is probably NOT a good idea to wear mini skirts. Cover the knees and stomach and you will avoid a lot of comments, attention and problems. If you wear it, tanzanians will typically think you are more or less asking for it and you might as well be prepared for a lot of comments and uncomfortable advances from men. Men CAN wear short, but again - leave the short ones a home and bring the longer ones if you can't live without them.
If you're going outside Mwanza to e.g. Sengerema, sleeveless t-shirts are not at all appropriate and you will never earn any respect with them if you don't tone down the clothing.