What are the risks of drinking tap water in Vietnam?

It's not safe to drink water directly from tap as there's a great chance the water is contaminated, you're most likely to get traveller's diarrhea by drinking that and least likely to get Cholera with a host of other lovely infections in between, some you can vaccinate against before leaving.

Just make sure to always boil the water you intend to drink (at least a minute will kill and deactivate bacterias and viruses) and never drink anything that's been opened, ditch the ice cubes and be suspicious of anything washed or uncooked. I'll quote the Canadian travel advisory for Vietnam on this, the US one goes in the same sense.

Food and Water-borne Diseases

Travellers to any destination in the world can develop travellers' diarrhea from consuming contaminated water or food.

In some areas in Southeast Asia, food and water can also carry diseases like cholera, hepatitis A, schistosomiasis and typhoid. Practise safe food and water precautions while travelling in Southeast Asia. Remember: Boil it, cook it, peel it, or leave it!

Hepatical and gastral infections, including a lethal outcome. Also liver damage because of iron remainders or chemicals after war possible dissolved in it