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: 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.
Visible crew/equipment: When Sgt. Hadley nearly throws Andy off the plate factory roof, the reflection of a boom mike is briefly visible in the shiny brim of Hadley's hat. Andy dropped the tar mop before approaching Hadley, and there are no other objects in this shot that could have caused the reflection.
Continuity mistake: When one of the "sisters" gets beaten up by Capt. Hadley he tries to escape from his cell and holds on to the bars on the other side of the passage. From the side his right hand grabs a diagonal bar, but seen through the bars he is holding on to a vertical bar.
Continuity mistake: When the warden is given a bribe by his contractor/buddy, it comes in a box containing a pie and the pie is in a disposable corrugated aluminium pie tin. The warden gives the pie to Andy in a later scene and when Andy and Red eat it, it is in a metal pie pan... the non-disposable kind.
Continuity mistake: During the scene where Andy and Red meet for the first time (baseball scene) the sun is in Red's face and so, Andy shouldn't have the sun in his face. But in fact, sometimes Andy has the sun in his face and Red doesn't anymore. Either they move very quickly between scenes or (probably) the whole scene were filmed at least two times.
Continuity mistake: In the same scene where Brooks is hanging himself, he carves his name and he is almost eye level with the spot where he is carving his name. The place where the rope is tied is lower. How come when he finishes carving his name he stretches to put the rope on? It is lower than where he was carving his name.