It isn't unusual to find errors in Household Exams, as they aren't "prime" records, they weren't created at the time of the event (birth, marriage, death). Once an error gets into a HE, it tends to be copied into future volumes. Besides incorrect birth dates, incorrect birth places are common. My GG Grandfather's birth record was the only record with the correct birth date, all other records had his christening date as his birth date. He may have not known his correct birth date!
Use Household Exams as a foundation, but find all the original vital records.
Oakland FamilySearch Library