Continuity mistake: When showing how Andy switches the books, watch the folder on the table. The folder has a corner that is bent up. When Andy removes the Bible and folder from behind his back and places then on the table, the folder he places has the bent corner. The one already on the table is perfectly flat.
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 out of is in the open air.
Continuity mistake: The sweat disappears from Red's white shirt as he approaches the oak tree at the end.
Plot hole: When the warden comes into the cell the morning after the escape, the poster covering the hole is fastened down on all four corners - impossible to do after squeezing into that small hole. [On the DVD commentary, the director confirms that this was a movie "cheat".]
Continuity mistake: When Norton prepares for his suicide you see on the desk a photograph and, a bit away, a lamp. After he has shot himself the photograph is leaning against the lamp (it was too far away in the previous shot to have fallen against it). There's some sort of card open on his desk on some paperwork which suddenly moves onto bare desk as well.
Continuity mistake: The "A" that Andy carves initially is different from the "A" shown near the end of the movie showing how he escaped.
Continuity mistake: As Norton kills himself, the glass that blows out behind him is quite large and about half of the frame gets blown out. There are a few specs of blood on the window as well. A couple of shots later as the camera pulls back and shows Norton you can see the hole in the window is quite small and shaped differently and a smear of blood above the hole now.
Continuity mistake: When Brooks has the knife to Heywood's throat, in one shot there is blood visible on his neck, yet in the next shot the blood is gone.
Continuity mistake: In the scene where the warden is tossing cells and comes to "size up" Andy, it shows all of the chess pieces on the window being knocked over while one is in the guard's hands. After a short time one of the pieces is upright again, without anyone touching them.
Factual error: Near the end of the movie, in the shot where the marked patrol cars are racing towards the prison to arrest the warden, you hear them using electronic sirens. Those sirens were not in law enforcement use until the mid to late seventies.
Factual error: In the scene where Andy first goes to work with Brooks in the library, the year is 1949 or 1950. Brooks tells Andy where the Louis L'Amour books are located. Louis L'Amour wasn't published in the US until 1951, and only had one book released before then.
Revealing mistake: In the scene where Warden Norton is loading his pistol, as he dumps out the bullets and loads them the primers are dimpled. Unfired bullets would not have the dimples from the gun's hammer (even if they were home made reloads, the primer would have been replaced).
Continuity mistake: Andy is discovered missing. While the warden is walking to Andy's cell, he tells the guard to question "him", meaning the Morgan Freeman character. He points to Freeman with his left hand but when the scene changes its point of view he is pointing with his right hand.