Overall, Florence is a fairly safe city. Perhaps the only problems to be aware of is opportunists whom hang around in the highly concentrated tourist areas, such as The Duomo and Santa Maria Novella.
When visiting Santa Maria Novella it is advised to stay between the Church/Museum and the river. Whilst the neighbourhood on the western edge of the Centro Storico and the south area of Santa Maria Novella is pleasant with magnificent views and buildings, the zone around the train station is run-down and less amiable. Please be careful if in and around this area, especially after dark. Do not travel alone but instead stay in groups if you are using the train station late at night.