When Don and Alan are having lunch, the water bottles on the table keep moving.
The rifle scope shows the postman's back as he is walking away from the sniper yet the dialogue states he was shot in the chest.
The position of Larry's hands changes between shots from in front and behind him during his chess game with Alan.
When Charlie, first draws the x and y axis. He puts the 'x' on the vertical axis, and the 'y' on the horizontal. However, on an actual graph the x-axis is the horizontal and the y-axis is the vertical.
Alan says you can't paint a Craftsman house in California because they are protected. This is incorrect.
Larry doesn't take his turn in chess before Alan puts him in check - Alan moves twice in a row. Also, from the position shown, there is no legal move Alan could have made to put Larry in check in any event. Finally, in the last shot of the scene, the position of both players' kings and queens have been reversed.
In the opening scene, heartbeats were heard (inferred to be the shooter's), which sped up as the shot came closer. Pro snipers are trained to control everything (from heartbeats to urination), because the slightest tick can result in a miss.