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).
Revealing mistake: When Tommy crumples up the test paper he had written for Andy and throws it into a waste basket the metal container shakes as if he had thrown something heavy. (Telling from the noise it makes the item must have been heavy.) (01:23:30)
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.
Chosen answer: In the original novella it is revealed that Andy smuggled $500 into the prison inside of his rectum. During an interview in 2004 Robbins incorrectly quoted the amount as being $100. The narration up until Red's release is provided as Red writes his account of the events while still in prison, and employs the same method to smuggle the story out. But since the issue of Andy smuggling in $500 into the prison isn't addressed in the movie, we should assume that he smuggled it in. In addition to this, the wardens scams are described as "near slave labor." From this we can assume that it is possible the inmates are getting paid (an incredibly small) wage. Perhaps Andy, with his financial knowledge, knows how to haggle, barter and stretch a dollar. One last (but not as likely) scenario is that Red allows some sort of lay by system to inmates.