Name of mother in school certificates do not have much importance in many places but if they entered once it should be correct in genuine and if there is any mismatch or incorrect spelling it should get corrected immediately.
Name,father's name,Date of birth are the basic details which required till our last breath for anything to be proved and they should be similar and a correct one in all documents. The school certificate for seniors and birth certificates for youngsters become a valid one. As the date of birth is deciding matters in one's life till his end,much care should be taken in the beginning itself. School certificate,college certificates,aadhaar,Pan card,voter Id, driving license should tally each other. You immediately approach in person to the college authorities and get corrected. No correspondences will yield good result rather than personal approach. Your delay will make the matter more delay.
The name,father's name surname etc., should be get verified even at the stage of collecting from school leaving itself as the same become base documents for the further studies as well for employment or anything.