Travel insurance: As still a developing country, Vietnam has several diseases, so besides bringing medicines, it’s better to buy insurance for yourself before you go, because all the medical safety advice in the world isn’t going to cover your medical bills if something does go wrong. You may refer to World Nomads for buying online.
First Aid kit. Now that you've gone to the trouble of getting yourself a whiz-bang first-aid kit, remember to actually take it with you. There's no point coming off that mountain bike at the top of the hill and realizing the bandages are all the way at the bottom.
Mosquito bites are the cause of most tropical diseases, so dress to avoid getting bitten – wear long pants and long sleeves, especially at dusk. Use mosquito repellent on any exposed skin, and sleep under a mosquito net if one is provided (or travel with your own if you are camping or staying in remote areas).
Beware of strong (or even not so strong) sun in summer time, especially if you are not used to it – you can burn or get heat stroke before you know it. Carry a hat and sunscreen in your daypack and remember to reapply the lotion after you have been swimming. Also drink plenty of fluids to avoid dehydration in hot climates.
The tap water is NOT safe to drink, except for those at the airport, big hotels & restaurants. Drink sterilized one or buy bottled water (making sure the seal on the bottle is intact).
Food. Beware of dishes that include uncooked produce (salads, fresh fruit and vegetables). Fruits that can be peeled (bananas, mangoes, etc) are generally safe to eat. Beware of frozen foods that may have been thawed and refrozen, and of undercooked meat, fish or poultry. When eating at food stalls, use your best judgment: if the food or preparation area looks dodgy, don't even consider eating it. If you are unfortunate enough to get diarrhea, the basic rule is stop eating and drink plenty of (bottled) water for a few days until it has passed.
No glove, no love. If romance happens along the way, practice safe sex. HIV/AIDS are quite widespread here. That means using a condom – and it's best to bring one from home, or else you may buy at the locality, so it's safe for you.
Beware of thieves. As in any country in this world, tourists should beware of thieves. In Vietnam, bus, crowded streets, festivals, exhibitions, etc. are normally ideal places for thieves to “do business”. Thus, be very careful with your precious stuff.