In the opening scene, Peter says he checked out three books by Stephen King from the library. In fact, The Body and The Shawshank Redemption appear in the same short story collection, Different Seasons.
When we see Peter/Andy's empty prison cell, discovered by Seamus the wooden pirate, there is no poster next to the Star Wars figurines; however when Carter/The Warden walks in there is one, into which he throws a rock.
In the beginning, Peter says he got three Stephen King books, "Stand By Me", "Misery", and "The Shawshank Redemption". The movie Stand by Me is actually based on the King novella "The Body"; The Shawshank Redemption is based on the novella "Rita Hayworth and Shawshank Redemption". Both novellas were published together in the book "Different Seasons". Not only are there no King novels titled "Stand By Me" or "The Shawshank Redemption", but Peter could not have checked out three different books from the library.
Peter says he picked up three books from the library: "Misery", "Stand By Me", and "The Shawshank Redemption". However "The Shawshank Redemption" and "Stand By Me" are part of the same book, "Different Seasons", so Peter would have only picked up two books.
When Andy tells Red, who he never met before, to go to Maine and get the box that he left there, the card says, "Red, do you remember the town in Mexico?" It is impossible for Andy to have left that box in Maine, during his time in prison, for he was in prison for more than 20 years, and couldn't have addressed the letter to Red before he was in prison because he never met Red. The card tells about the town in Mexico, which shouldn't have been mentioned since he never planned that trip until he was in the prison.