What kind of a doctor error birth can lead to cerebral palsy?

Usually none: Most cerebral palsy isn't due to a medical error but rather to inherited medical conditions.

Who knows: Karen Nelson & others published data from a review of >30,000 births in the late 70's. She showed more than half of CP cases where symptoms were evident by age 7 had a normal pregnancy, labor, delivery & 1st 3 yrs of life. We worry when babies are deprived of oxygen at delivery & if any doctor decision places baby at risk. However, the real origin of CP in a specific case is often unknowable.