Humans have more dental problems than Animals

Bad teeth are a common trait in humans because humans have a very poor jawbone layout, teeth that are in heavy evolutionary flux, and an exceedingly adaptable bite.

The human jaws are too small to contain the full human dentition. This is why most people need to have third molars extracted. We're also rather unique in that our teeth take up the entire jaw space, whereas most animals have large spaces without teeth that can provide extra room for teeth to come in.

A number of our teeth are not genetically "stable." By that, I mean that we have a high likelihood to from birth be missing teeth, have deformed teeth, or have extra teeth. The third molars are often completely or partially absent. The upper lateral incisors (teeth on either side of the middle top teeth) are often missing or mis-shapen (Google "peg laterals" for more). Even the two center upper teeth sometimes duplicate (Google "mesiodens" for more on that).

The temporomandibular joint (jaw joint) is the most complex and most adaptable joint in the whole body, allowing us to cope with, if you'll excuse some dental jargon, shockingly fucked up teeth and really screwed up bites.

So why is all of this so common in humans?

We don't rely on our teeth to survive as most other animals do. A cat with messed up teeth can't catch food, and will die before reproducing. A human will compensate with hands or with tools.

Nature only needs our teeth to last ~30 years. That's enough time to reproduce at 13/14 and then raise the children to reproductive age (another 13/14 years). For this reason, that's why without dental care, 30 years is about how long our teeth last on a rough caveman style diet. That's also why most people don't run into serious dental trouble until their 30s or 40s.

Simply put, by enjoying soft processed diets, practicing dental care, and by avoiding tough raw foods like raw meat, bone, seeds, and roots, heavy duty, well-constructed teeth are not needed and are wastes of energy. Since good teeth are not an evolutionarily important feature in Homo sapiens, genetic errors are not selected against, and the whole dental apparatus (teeth, jawbones, etc.) falls to pieces and accumulates defects. 

Give it 100,000 years without genetic therapy and the teeth of Homo futuris will be an ungodly mess.