Generally Mombasa is one of the safest towns in Kenya, thats because of the tourist industry, but still every week someone is killed by muggers.
The Kenyan authorities are not doing enough to reslove the problem. Majority of the incidents happen to rich local businessmen rather than tourists.
Saying that a couple of years ago raiders raided a hotel late at night, stole everything from the hotels safe deposit box and shot the guard. Most hotels in mombasa have safe deposit boxes at reception rather then in the rooms.
So don't flash your cash in or outside your hotel, don't wear any jewelrey, never walk on the beach at night or in secluded areas.
Prostitution is big in mombasa, and 2 in every 5 prostitutes are infected with AIDs
Do not use drugs (GANJA). They will ask you to join them but don't.
You never know if it is a policemen off duty who is trying to frame you for bribe money.
Also you really don't want to go to a kenyan prison...
Never use a telephone in a hotel, normally in a hotel it is always a bit more expensive but in mombasa it is crazy how much they charge in tha hotels.
Best thing is to go to a local village, and go to a "phone central" (don't expect a big building, it is just one room with a person on a table)
They are really helpfull and sooo cheap.
(be aware to most countries is 3 minutes the maximum you can call)