Continuity mistake: In the first of the nightclub scenes in which Dorothy Vallens is seen singing 'Blue Velvet' her dress mysteriously changes from having straps to a halter top. The 'why' for this becomes clear later in the film - in her second nightclub appearance (the following day) she is wearing the halter top. Evidently the filmmakers cut in a shot filmed for the second scene.
Continuity mistake: When Jeffrey is caught by Dorothy in her apartment, she cuts his face with a knife. In the next scene, the following day, there is no mark on his face when he's talking with Sandy in the car. But in the scene after that, the cut is visible again.