When Mrs. Baker's face is first seen, her lips have no color, and in the next shot, her lips look like Daphne's: colored. When she is at the doorway in another shot, her lips are not colored again.
Batman's tights disappear before they leave to go to the bat-copter and reappear the next time you see him.
When the Mystery Machine leaves the Batcave, the letters on the van are spelled backward.
As the Joker and Penguin were being interrogated, a shot of Velma is seen and her glasses are white. In the next shot of her, her glasses are black again.
In one scene, Batman is seen reaching around and his right hand is bare with a ring. In the next shot of him, his hand is gloved again.
Batman's neck is visible on his costume throughout the whole story, unlike the standard depictions of his suit in most of his other mainstream appearances.
It was probably just a natural reaction, but Fred reacts with great astonishment to the phony money as if he's never seen that before, which he had several times in Scooby Doo, Where Are You! (1969).
Fred calls his teammates "kids," which is what they are normally called by villains, but not by themselves.