Revealing mistakes: Wires can be seen when The Wizard is supposed to be invisible, most notably in the telephone booth when The Wizard is on the run and calls his headquarters.
Revealing mistakes: When some of the remote-controlled cars are supposed to be run without drivers, the stuntman can be seen slumping low in the seat.
Plot holes: For three chapters, Robin tries to persuade Batman that the professor can't be the Wizard because he's a wheelchair invalid. In the 14th chapter, we see the professor up and walking about, even in front of Batman and Robin, with no explanation whatsoever, and no questioning on Batman and Robin's part.