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: The cane of the 'mysterious' drunk that happens to be not too far from Thorne's table is hovering instead of being properly hanging off the edge of the table in a couple of shots. (00:03:00)
Revealing mistake: Harvey Dent has been poisoned. Commissioner Gordon picks up the phone; there's a mistake in the animation here, with the telephone cord clipping through. (00:08:50)
Be A Clown - S1-E11
Revealing mistake: When Mayor Hamilton Hill speaks to his geriatric butler as he is tying up the birthday banner, the butler's right hand is miscolored in some frames and becomes part of the banner, same purple color. (00:03:55)
Be A Clown - S1-E11
Revealing mistake: At the beginning of the shot with the creepy clown that sends his unicycle crashing and begins juggling, the kids in the background are frozen in place for the first frames, then start moving. (00:05:15)
Be A Clown - S1-E11
Revealing mistake: When the tied up Batman is forced to emulate Houdini, he draws the air that will last him for the two minutes of his act while water already submerged his face. (00:15:15)
Revealing mistake: When Alfred proudly shows the sketch with his joke, the top part of the shower pipe disappears in some frames. (00:03:15)
Revealing mistake: When the paper with Harvey Dent's picture on the hospital bed is burning, there are a few frames with the words "CUT THESE FRAMS" [sic] that can be seen through the flames. (00:20:30)
I've Got Batman in My Basement - S1-E20
Revealing mistake: The two kids grab a couple of items from Sherman's detective box, but the items never go away, a duplicate is spawned instead. (00:03:30)
I've Got Batman in My Basement - S1-E20
Revealing mistake: Sherman puts down the Jr. Detective box to try to get back the stuff the bullies grabbed. He sets the box on one of the steps, but the way it is drawn defies gravity. (00:03:40)
I've Got Batman in My Basement - S1-E20
Revealing mistake: The thief kicks away the canister bird seed was falling on...and the bird seed keeps landing in the same spot, which at this point is thin air. (00:05:10)
I've Got Batman in My Basement - S1-E20
Revealing mistake: Penguin grabs the umbrella from the floor. For a moment you can see two umbrellas, and in the next shot the top with the smashed rotating blades is fixed. (00:19:50)
Revealing mistake: When the passengers are evacuating the sinking ship after the bomb goes off, there is a shot shown from above, of passengers running up the stairs. Many of the character designs for the passengers are repeated throughout the shot. For example, a blonde woman in a purple dress can be seen three times in the shot. (00:02:36)
Christmas With the Joker - S1-E38
Revealing mistake: Batman and Robin, thanks to the Joker's generous hint, are at the toy factory. In the wide shot just before the phrase "Look sharp, Robin", look at the shadow on the ground; Batman's cape deflates, but the shadow does not move and is still just as wide as it was before. (00:17:10)
Answer: She escaped off-screen and created a copy of herself to fool everyone.