Continuity mistake: Trying to protect Salvo, Riley punches two thugs. The second one is a red bearded man. The big boss urges then the other baddies to attack, and redbeard is way behind him, hasn't leaped into action yet. (00:11:35)
Plot hole: Alfred manages to find the bad guys because not only they grabbed the supposedly homeless guy off the street (Bruce in disguise), but also somehow brought his car to the scrapyard. If they knew it was his, they would have known something was off (a hobo with a car?) and they would have not got rid of it after more than a day. If they didn't, and they just towed out a random car, Alfred had extraordinary luck - nothing in fact would lead to believe that the truck was even related to the car.
Continuity mistake: The 10/6's on the Mad Hatter's mind control cards come and go throughout the episode.
Continuity mistake: The 10/6th on the Mad Hatter's mind control cards come and go throughout the episode. An example is when he first is shown holding them they're blank. Then when he decides to use them on his date with Alice they've suddenly got the 10/6th.
Continuity mistake: When Jervis Tetch is shown he's around 5'5 maybe with blue eyes and sandy white looking hair. Yet the day after his night out with Alice he's suddenly around Bruce Wayne's size with blond hair and his eyes are no longer blue.
Factual error: A vital part of the plot's resolution is based on the fact that the reading activity of the brain happens in the right hemisphere, while the dream activity is localized in the left half, making thus impossible to read during a dream. Besides anecdotal experience that says the contrary, this 'fact' is not supported by medical studies, which in fact contradict it. There is no hard distinction, it varies greatly between individuals and even going by those studies who could be seen as supportive of the theory, reading would not be impossible and speaking would be just as hard.
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: 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)
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: 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: 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: 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: 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)
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)
Continuity mistake: Both Selina's, once she's been mutated, and Tygrus' noses change color. Hers goes black briefly when she finds Batman in the forest and Tygrus' turns grey briefly as Dr Dorian scolds him.
Continuity mistake: Scarecrow's shoes are light brown in most of the episode. Yet once he's back in his cell they're suddenly dark grey.
Character mistake: The Scarecrow's thugs flee as his water pump machine explodes, yet he seems to have stuck around long enough to be affected by his own toxin.
Continuity mistake: When Batman stops the countdown it reads as 1:45. When Scarecrow starts it back up it's suddenly 0:14.
Plot hole: It's never explained: 1. How or who helped Scarecrow escape from his cell or 2. Why he'd be sitting in there at the end in costume instead of prison garb.
Suggested correction: Something not being explained is not a plot hole. The manner in which Scarecrow escaped his cell isn't essential to the plot, and therefore doesn't require an explanation. And the reason he's left in the cell in his costume is for the same reason Batman was left wearing his outfit when he was imprisoned: because the doctor at the asylum felt removing his outfit in his hallucinatory state could cause him to become catatonic.
Continuity mistake: Scarecrow's pants turn red when he's on the catwalk turning on the pump machine.