In the car after Wednesday sends Shadow shopping, Wednesday gets upset about the cell phones and throws them out the car window. However, when shopping, clearly written on the shopping list is: "2 CELL PHONES".
During the checkers game, when Shadow plays his last move, his hand is seen as coming from the opposite side of where the pieces are. Problem is, it's Czernobog who's sitting there.
When Mr. Wednesday sends Moon to do some shopping, the price signs in the store are clearly the distinctive ones used by the Canadian department store Canadian Tire, which was used as a filming location. Many of the products visible in shots are Canadian brands like Alcan aluminum foil.