Havana is an amazingly safe city, and the heavy police presence on the streets keeps it so. You can walk through areas here in the middle of the night that you wouldn't dare enter midday in places like London or New York. However, watch out for young men on bicycles who try to snatch purses, handbags or cameras. Like anywhere in the world, pickpockets are active on crowded city buses.
Don't stop to talk to anyone offering 'Havana cigars' on the street, as these are the most persistent hustlers around. Shops may try to overcharge or cheat you, especially if your Spanish is minimal. Verify all prices before buying, check the addition and count your change before leaving the counter.
Environmentally, crumbling sidewalks with big holes can be a problem, and the air pollution is irritating. Take care walking on La Rampa when it rains, as the slick sidewalks throw people on their backsides regularly.