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. (02:14:40)
Other mistake: When the warden is questioning the night guard in Andy's cell the morning-after the escape, he rips the clipboard out of his hand and hands it to Hadley. The pencil is stuck to the paper but is not under the clip. The pencil would have flown off.
Factual error: The sign for Buxton is horizontal with two poles. Signs for Maine towns are vertical and mounted on a single post.
Continuity mistake: When Hank Williams is singing "Lovesick Blues" the MGM label is from 1968. This is meant to be 1963.
Factual error: A single bar of prison-issued soap and a pool of cold, sewage-contaminated water would never be enough to wash the stench that Andy would have acquired from worming through 300 feet of waste.
Suggested correction: Andy could have found an area of cleaner water (say a puddle, small pond, or other ditch) to do a basic cleaning before fully cleaning elsewhere, like a cheap motel.
Suggested correction: First of all it was 500 yards, not 300 feet. Second, all Andy really has to do is go upstream to where the water is clean. I guess you must have also forgotten that has been raining.
Revealing mistake: When Brooks is carving his name, "dust" seemingly like plaster dust vs wood dust is shown falling on the table top, his shoes etc. When they cut to the view of Brooks looking at his work and closing his knife, there is no "dust" on his hand or knife. That much carving with that much dust falling on the table would have left his knife covered with dust. It was clean.
Continuity mistake: The warden pulls out a box of Remington .38 Special cartridges to load his revolver prior to his suicide. The warden empties the cartridges on to his desk and loads the revolver with what are Winchester/Western cartridges.