Factual error: At the end of the film following Andy's escape from Shawshank there is a scene of him driving along the cliff edge in a red car. This car is a red Pontiac GTO from 1969. The year in the film is 1966, 3 years before the car was made. Confirmed in commentary. (01:57:45)
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)
Factual error: In the scene where Red is working in the Food-Way shortly after his release in 1967, there are cartons of "More" and "Newport" brand cigarettes visible on the shelf to his right. "More" was not released until 1975. (02:09:25)
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)
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)
Character mistake: Red says that Andy crawled to freedom through 500 yards - 'just shy of half a mile'. 500 yards is far less than half a mile; in fact, it's less than a third of a mile. It is however just shy of half a kilometer, which may be what King was thinking of when he wrote the book.
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.
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.
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: Chess is played with a white square at the right end of the first row. You see the chess board with the stone figures in Andy's cell, and every time there is a black square on the right. Andy would have known better.
Continuity mistake: In the scene where Brooks Hatlen is committing suicide you see him engraving "Brooks was here" into the wood panel near the ceiling. The table he is standing on puts his face opposite the vertical wooden bars underneath the engraving (we see this in a shot looking up at him through these bars). Then when he rocks to tip the table over to hang himself he doesn't seem to fall at all, maybe a few inches if anything, yet when we see the pan out he has fallen at least 2 feet.
Factual error: In the courtroom scene there is a microphone - a 1955 Shure SM55. The courtroom scene was set in 1947.
Continuity mistake: The "A" that Andy carves initially is different from the "A" shown near the end of the movie showing how he escaped.
Factual error: In the scene where the guys are drinking beer on the roof, the bottles have "ribbed" tops. Beer bottles did not have twist-off's in the late 40's.
Factual error: Red, while using the restroom in the grocery store he worked in after getting out of jail, is peeing in a 1980s urinal.
Other mistake: When the cons are drinking beer on top of the roof, the man that finished his bottle gestures for another. The guy takes out an already-opened bottle of the bucket horizontally, the beer should've poured out.
Factual error: When Red is working in the grocery store after his parole, as a bagger, the cashier is using a National C100 register, which is a non-itemizing register. This wouldn't be usable at a checkout in a grocery store, as the customers usually have multiple items.
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.
Chosen answer: He probably only knows the name. He doesn't want to know anymore, so he can pin the blame on Andy should anything go wrong. He no doubt hasn't even considered that Andy might have ID so he can access the accounts after his escape.
Grumpy Scot
Also, Andy indicated that the deposits were night deposits, which were in envelopes. So, the warden may not have known the "Randall Stevens" name.