We did train travel in Italy last October. The situation didn't seem that bad as I observed. Take caution to your personal belongings as you usually do when travelling in a foreign country should be good enough. However, public safety gets worse as you go more south.
If you decide to do train travel, do not take any chance to save money because the train conductor always checks your ticket. Also train travel in Italy requires seat reservation. If you can plan your trip well ahead, you could save lots of time and get the class you want. Please check Eurail's website for detail on reservation.
In Italy, especially in Rome, restaurants may charge you the bread they serve, even you didn't order it. If they do charge you the bread, it's okay to leave little or no tip.
Museums in Florence require reservation, so make it in advance if you want to take a look. Venice is a maze, so make sure you have a map and sufficient time to go around.