Like any other large tourist centre, Florence has a high rate of petty crime. There are three common types of theft: pickpockets on the bus, especially at rush hour; bag-snatching, where the thief, on a scooter, grabs the victim's hand or shoulder bag violently as he passes.
Thefts in the historic centre especially while waiting in a queue to enter a museum or church. Here is some advice to minimize the possibility: be particularly cautious while travelling by bus; do not keep large sums of money, traveller's cheques, credit cards or personal documents in your bag; if you find you have to wait for any length of time in one place, keep your camera in your hand and be very wary of anyone who approaches you without clear reason.
Obviously it is preferable to change small amounts of money at a time and to use a bank to do so. Police phone number