The risks depend on the kind of treatment and how long a patient has braces or an appliance in. If you have any concerns, please talk to your orthodontist. Here are a few common things that can happen:
Cavities - it is harder to keep teeth clean with braces on and cavities can form around the brackets. White spots, which are the start of cavities, can also form. Invisalign or other removable trays are a good option if a patient is worried that they will not be able to keep things clean.
Root resorption - Moving teeth requires putting a force on them with the wire. If too much force is used or the force is used for a really long time, sometimes you can get root resorption of your front upper and/or lower teeth. Root resorption means that the roots of your teeth get shorter. If there is any concern, your orthodontist will keep track of this with a few x-rays throughout treatment. Now, more and more new bracket designs are being used that put very small amounts of forces on teeth, such as self-ligating or Damon brackets.