Crime rates in and around the tourist areas are relatively low, thanks to an increased police presence and "neighborhood watch" campaign by business owners.
Santa Monica is considered to be Southern California's "Home of the Homeless" a title shared with Hollywood; the city has amongst the highest per-capita homeless populations in Los Angeles county although lessened by recent police crackdowns. However, most of them are harmless. You will probably be asked for spare change when traveling on foot, but you will probably not be bothered further a suitable response would be something like "nothing today" or "nothing at all" depending on the temperament of the one making the petition.
Just use common sense and stay in the main tourist areas if you decide to go out at night.
The area of Santa Monica presenting the most safety problems is the small neighborhood around Pico Boulevard and 20th Street. Side streets in this area are best avoided at night.