The Tale of the Dream Girl - S3-E10
Revealing mistake: A kid running through the bowling alley moves aside to let Johnny, who is a ghost only his sister can see, pass by.
Heart of Ice - S1-E3
Revealing mistake: When Batman - disguised as a security guard - opens his utility belt, the belt opens and shows a configuration of buttons and a split-second later, a key card materializes out of thin air in front of the buttons. (00:11:30)
Revealing mistake: When Roberta Halton knocks Rob unconscious, you can see that the blunt object barely even makes contact with his head.