The position on the chess board in the opening scene is noticeably different from the position on the board when Cooper explains the importance of his game with Windom Earle to Sheriff Truman.
When detailing his experience with Windom Earle, Coop keeps changing his pronunciation of the name 'Caroline' to either "Carol-LIN" to "Caro-LINE"
The body bag that is wheeled out of the sheriff's office is white, with two black belts. When it leaves the building, one can see a brief glimpse of a black bag with two blue belts.
When Andy struggles to remove his left glove, at around 12 minutes, it clearly falls vertically down to the ground. But, in the next scene, it is shown to have flown over and stuck to the glass panel in front of Lucy, which is impossible.
When Andy enters the room, he says, "Sheriff Truman. Agent Cooper." Cooper is still suspended from the Bureau and has been deputized by the sheriff. Andy should have said, "Deputy Cooper."