Two dimensional normal rings Let $R$ be an algebra finite type over a field $K$. Assume that $R$ is integral, Gorenstein and $\dim R=2$. Assume furthermore that there are only finitely many maximal ideals such that $R_m$ is not regular.
Then is it true that $R$ is normal?

Yes, This follows from the Serre's $R_1+S_2$ criterion for normality.
($R_1$): the ring is regular in codimension 1.
($S_2$): we have $\mathrm{depth}(A_{P})\geqq \mathrm{inf}(2,\mathrm{ht} (A_P))$ for prime ideals $P$.
In your case, Gorenstein implies Cohen-Macaulay and such are $S_2$, and at most finitely many nonregular closed points implies $R_1$.
