There are relatively few health risks in Ho Chi Minh City. You will want to take the standard precautions when traveling in less developed areas: avoid unwashed fruits and vegetables, water from unknown sources and unrefrigerated dairy products. Most hotels will provide free drinking water in your room.
Perhaps the most serious risk to your health is the heat. In Ho Chi Minh City's tropical climate, you need to drink plenty of fluids and give yourself some shade from time to time.
Safety & Security
By far, the biggest threat to your safety will happen when you cross the street. Almost everyone in Ho Chi Minh gets around by motorcycle, with it seems little regard for their own safety. A red light is no guarantee that motorists will stop. Some will invariably honk their horns and proceed to drive through cross traffic.
The best way to achieve a safe crossing is to first follow your mother's advice and look both ways before stepping into the street. Once you see a relatively clear path, proceed slowly across. This gives the cyclists time to see you and steer out of the way. Running is definitely ill advised.
Several guidebooks report problems with "snatch and dash" thefts, although we have never observed such things. You of course need to take care with your valuables and watch out for pickpockets.
Cylco and motorcycle taxis can be a particular annoyance. They seem to assume that any westerner who walks down the street instead of using their services must be lost. They will ride alongside you for blocks pestering you to use their services to show you around. Even if you do avail yourself of their services, don't expect the sales pitch to stop there. We've heard numerous stories of cons and outright robberies by these guys.