My parents died last year and gave me their house. The property taxes are very low because of the over 65 tax exemption and the low school taxes which occurred 20 years ago. The appraisal district has not changed ownership for the property even though a deed was filed at the courthouse. Should I just pay the lower level of taxes?

It is highly likely the appraisal district will discover the error at some point. If they do, they will assess you the taxes for the difference between what you paid and what you should have paid. You are probably better off correcting the error with the appraisal district.