Their might be a problem in the future. Many time 10 , 10+2 certificates are taken to be the legal documents . So if you can do rectify the mistakes by contacting a lawyer and producing an affidavit or by the procedure for rectification as suggested by your board.

Hello,

For most of the document verification they require your class 10 marksheet certificate so you should carry on with that for future purposes. Furthermore, your mother's name is not that important as compared to your father's name or your name during verification so you shouldn't worry about that.

To be on the safe side you should write a letter to the concerned authority regarding the matter and request them for the marksheet to be corrected. Most probably it will be corrected.

Hope this helps