Improper use of forceps can potentially cause damage, but it is relatively rare. Doctors usually use a vacuum method when birth assistance is necessary. It is considered to be safer.
Forceps should only be used as a last resort. Brain injuries as well as facial deformations can and do occur with the use of forceps. If a baby is stuck in the birth canal and it is too late for a c-section then forceps should be used with caution.
Forceps can be used to speed delivery. They are clamped around the baby's head and incorrectly used can cause bruising or crushing of the skull and face.
Sometimes they have to be used when it's hard for the baby to come out. Most of the time they only leave bruises on the baby's head and they don't cause real damage.