Continuity mistake: The gang find Jonny tied up in a chair and he says it wasn't a publicity stunt. Both his arms are tied up to his sides by the rope. It cuts from the close up to show them all again, and suddenly Jonny is holding his hand to his head and Fred is suddenly pulling on the rope, his arm outside of the rope. (00:02:45)
Other mistake: There is a scene where the gang is the home of the Bank President, just after dropping off the injured bank guard. At one point the Bank President is standing behind an end table of some kind with a lamp on it. Even though there is nothing underneath the table to block your view you cannot see the lower part of the Bank President's leg. It looks like it has been cut off.
Continuity mistake: After the mystery is solved, the gang are driving away in the Mystery Machine. Shaggy and Scooby are in the back marveling at their wax dummies. Velma, Daphne, and Fred are in the front seat and can look back at them. But when it shows an angle from in front of them, the inside of the van behind Fred, Daphne and Velma can't be seen, only a solid gray wall where you should see Scooby, Shaggy, and their dummies, and even the back doors of the van. (00:20:50)
Continuity mistake: Fred begins telling the gang his plan for trapping the Wax Phantom. They are standing at a window with Fred on the right, Daphne in the middle, and Velma on the left with Shaggy behind them. It cuts to a view from behind, and suddenly Daphne and Velma have switched spots, and Shaggy is off to the side. (00:17:15)