I guess it is less of a hidden danger and more common sense, but if you are going to be visiting the Museo La Venta or walking around the park areas, you should be aware that the mosquitoes in the area are relentless.
There will be a few people outside the museum selling repellent, but it may be cheaper for you to buy/bring your own in advance. Once you enter the park area, the little bloodsuckers in the thick jungle greenery and stagnant swampy water are too thick to swat away. Long pants or shirts are recommended if you can stand the heat, but repellent is also a must.
Be careful when driving for the first time in Villahermosa. The drivers here are really impatient and daring, and every drive is a harrowing experience. It's typical for people to make a left turn from the right lane, create new driving lanes when none exist, and no one expects, and even gets upset, when they have to stop for a traffic light for more than 2 lights, as during rush hour. So unless you want to get bumped in back, after the second green light, go through even if it again turnms red, and say your prayers!
Currently there is a lot of drug trafficing problems in the area. The police have been ambushed several times and many execution style murders happening weekly.
I always feel safe walking in Villahermosa, the people are friendly and there doesn't seem to be much violent crime, except between the drug runners and police. So just be aware that you do not get caught in the middle.