Continuity mistake: At the start when Andy opens a bottle of alcohol, he drinks it with the same hand he opened it with. His hand is shifted after the second time we see him take a drink. (00:03:00)
Suggested correction: Watch carefully he takes the cap off and palms it in his right hand and as he does, so he lowers his hand and grabs the glass bottle to have a drink.
While the mistake isn't very clear, this mistake seems to be about the second time we see him take a drink, after the cut. After he says it's inconvenient the gun was never found, he's seen lifting the bottle by the neck, then the next shot, he's holding it further down.
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. (00:24:00)
Continuity mistake: When Andy is talking to Red for the first time in the yard, Red is playing catch with a few guys. Towards the end of the conversation Red catches the ball twice without throwing it back the first time. (00:25:00)
Continuity mistake: When the convicts are having beer on the roof you see Red taking a sip. The camera cuts to Heywood offering Andy a beer, and when it cuts back to Red taking the next sip his bottle is much more full than before. (00:36:55)
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. (00:43:15)
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. (00:48:30)
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. (00:54:15)
Suggested correction: It was always there. But in the 3rd of 4 scenes it was significantly more visible as a bright red streak. The other 3 times it's a dark red dot near the knife point.
The amount of blood changes from scene to scene, not just how visible it is.
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. (01:00:25)
Continuity mistake: When Andy is playing the opera music, the whole prison stops what they're doing and stares at the speakers. When they show the infirmary, an African American man gets out of bed and looks out of the window. When the camera goes to the prison yard it pans around and goes right across the same African American man, who is now standing in the yard. (01:06:05)
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. (01:45:45)
Continuity mistake: In the two different shots we have of Tim Robbins getting ready to put the book and folder into the safe for the last time (before he escapes) he collects the book and folder in two very different ways. First time he pulls the book towards the folder. Second time he brings the folder to the book. (01:49:55)
Continuity mistake: When Andy is in the bank, in the background you can see a man in a "porkpie" hat and a white shirt move forward to talk to the cashier. As Andy stands up to leave, the man can be seen again, standing towards the back of the queue. (01:56:10)
Suggested correction: The man may have made an error to some paperwork (deposit slip or withdraw slip), and had to get another one and fix his mistake...which would have put him at the end of the queue. You don't get to jump back in line, unless offered that convenience.
Continuity mistake: When Norton loads his gun the bullets are scattered over the table. When he takes aim the bullets are neatly in one place, but after has has shot himself they are scattered as before. (01:56:45)
Continuity mistake: When the warden shoots himself, he places the gun on the middle of his neck but when we see him lying there the bullet hole is now on the left side. (This is corrected on the tenth anniversary edition. The director also confirms this change on the DVD commentary.) (01:57:00)
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 also some sort of card open on his desk on some paperwork which suddenly moves onto bare desk and gets shorter. (01:57:10)
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. (02:03:40)
Continuity mistake: The sweat disappears from Red's white shirt as he approaches the oak tree at the end. (02:06:10)
Continuity mistake: When Red finds the metal box he takes out an envelope in a plastic bag, folded up on the right side. When he opens it the crease is on the left side. He hasn't turned it over. (02:07:30)
Continuity mistake: When Red is walking along the beach before he meets Andy his hat flies off and almost lands in the water. In the next wide shot the hat is lying a few meters inland against the direction of the wind. (02:10:30)
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.