Answer:
Although Qigong and Tai Chi are miraculous healing systems, if done incorrectly they can have many negative consequences (which unfortunately is moderately common in the field, especially outside of China).
A Tai Chi Master, Bruce Frantzis authored a book titled "Opening the Energy Gates of Your Body" explaining one of the fundamental qigong forms that links into Tai Chi and every other Taoist practice. To combat the trend of "bad qigong" he added a section on how to not practice. To paraphrase a few parts:
The essential theory or idea is that when one does Tai Chi and Qigong, one should never strain or force anything to happen and stay within 70% of their total capacity. If this rule is followed, very few problems can occur-the vast majority of negative effects occur in people who practice Tai Chi or Qigong forcefully strain. Similarly, if something starts to hurt or feel as though it's being damaged, the best course of action is to stop.
The most likely negative effect of Tai Chi and Qigong is that a body part (especially the knees) can become damaged from being over strained due to movements being done with bad internal alignments that damage the body part. If alignments are taught properly (one of the main subjects of the Energy Gates book), this never happens.
If advanced Qigong or Tai Chi is done with an unqualified teacher who is not aware of common pitfalls to avoid, people can become mentally unstable (up to and including become crazy) as a consequence of their internal energy pathways becoming deranged.
Most of the other problems I know of are extremely rare, and the vast majority of the time Tai Chi is one of the most effective healing arts that can be studied for nearly any condition. However, that doesn't preclude it from being done with a bit of common sense! After all, any sport with movement requires basic precautions to avoid injuries.