Not many. Cryotherapy is based on the fact that frozen tissue dies. Most non-malignant problems of the cervix, due to the papilloma virus, can be treated as local issues. Removing the local tissue does not kill the virus but it eliminates the portion of the cervix which has been stimulated to grow abnormally. The frozen tissue breaks down, producing a thick discharge but complications are rare.
Scar Tissue. Cryotherapy on the cervix can sometimes cause scar tissue on the cervix making it harder to open in labor. A typical scenario for someone with this is a woman who presents in labor with strong, frequent contractions but whose cervix is stuck at one centimeter for hours, then suddenly she is six centimeters dilated. This happens when the scar releases. It just takes time and patience.