Continuity mistake: Alfred is skilfully dancing while sitting and sipping tea. The radio rests next to a circular monitor on the computer. Then on a featureless spot, then directly on the monitor itself. (00:04:05)
Continuity mistake: Batman blasts the last door between himself and the villain. The floor is in frame for a lengthy time and there's no trace of debris, but in the next shot Batman passes the remains of the door. (00:20:35)
Continuity mistake: Gathering evidence inside the Sewer King's lair, Batman's camera changes size (it gets bigger) and shape (the button is on the left but it started on the right). (00:15:55)
Continuity mistake: The content of the table of the Sewer King constantly change when he has his messy dinner. At the end he flips the table and throws everything on the floor, and the floor is clean a second after, even. (00:12:35)
Continuity mistake: The policeman that writes down the woman's leprechaun sighting is using a brown and yellow notepad in the first shot, which turns into a white paper sheet in the next. (00:03:05)
Continuity mistake: When the Matron fails to draw the taxi's attention, a couple passes by her (she wears a blue raincoat and a purple beret) but they were nowhere in sight in the wide angle. (00:02:45)
Other mistake: The kids need sunglasses to be in daylight, since they have been segregated into the darkness of the sewers for so long. For the happy ending though, only the first one has a moment (very brief, considering that Frog still needed them at Bruce's) of squinting, eye-rubbing and discomfort. The others are instantly fine already the moment they are pulled out of the manhole. (00:21:35)
Other mistake: Batman sees the robbery happen, but he has yet to start his chase when the rotund old lady is deep into discussion with the policeman. (00:03:00)