Doctor Detroits hands are in a different position between shots. When he initially jumps aboard the tow truck, he uses the side-view mirror as a handle. In the next cut, he is shown holding on to the window frame.
The goof item below may give away important plot points.
When Cliff wins the sword fight against Mom, and puts the end of his sword at her chest, you can clearly see the tip is very blunt. In a following scene, Cliff thrusts the sword upwards into the ceiling, without the blunt tip.