Factual error: When Red is sitting under the oak tree in 1967 and pulls the money out of the envelope, the top bill is signed by Nicholas F. Brady, who was Secretary of the Treasury September 1988 - January 1993. It's less about reading the handwriting as noting the different appearance of different signatures from different eras.
Factual error: Towards the end of the movie when Andy is escaping, he breaks open a sewage pipe and is covered with its contents. It is physically impossible for the sewage to shoot out of the break like it did. In order for that to happen there has to be pressure. But there is none there, because the end he crawls through is empty and the end is in the open air.
Factual error: In the library, Heywood is listening to Hank Williams' "Lovesick Blues." He is playing the double LP "Hank Williams 24 Greatest Hits," which was originally released by MGM in 1970. "Lovesick Blues" was recorded long before this, but it is not possible for him to have acquired that particular 1970 double LP.