When Murray mentions Joe's graduation shot, a photo appears and Murray then points out that Joe is the one with the hat. However, in the photo, no one is shown wearing a hat.
When Murray is behind the desk, talking about the start of his mobster life, there are all sorts of items scattered on his desk. However, when the film cuts away and then returns to him on the desk, the orientation of the various items on the desk has changed, including the folder of papers that originally was in front of him.