Continuity mistake: At One Eyed Jack's, when Agent Cooper and Jacques are sitting and talking there are 2 glasses of beer on the table. In one shot Jacques finishes a glass. When he gets up, both glasses are full.
Continuity mistake: When Cooper is at the police station describing the events of the night of the murder, he is seen taking a doughnut and placing it on the napkin next to him. A few shots later his napkin is empty and the doughnut is back on the stack.