Can mild cerebral palsy have mental or physical limitations?

Maybe: Mild cerebral palsy will not have any significant mental limitations. Physical limitations are dependent on the level of involvement.

Hard to say: Cerebral palsy by convention implies an injury to specific areas of the brain controlling motor movements.If other brain areas are affected by the same event, other issues can be linked.This includes more likelihood of seizures, learning, etc. The milder the CP the less likely other areas that control speech, personality, learning, etc. But it is still possible.