Be A Clown - S1-E11
Other mistake: The cards that Jekko the Jokester throws at Batman have in one shot ("Now it's my deal") numbers that do not match at all the symbols. (00:13:40)
Be A Clown - S1-E11
Other mistake: When Jordan comes out of the truck, something went wrong with perspective and/or proportions, because with his leg bent he is practically as tall as the truck door, and he's a child.
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.
Other mistake: Bruce remembers who he is, which somehow gives him also the strength to bend metal (!) and escape. A new prisoner is carried in the camp by the guards, but...he's not new at all. He was already there the first day, standing in the group of prisoners that was eating. And the guy who escorts him is the same that less than a second later spots Bruce from the watchtower and blows the whistle. (00:06:20 - 00:14:30)
Plot hole: The two agents split; the rookie goes down an alley, chasing the two henchmen, who reached their car and chase him back down the alley almost running him down. Batman saves him though, destroys the car and quickly interrogates a suspect. Somehow though he also manages to save Montoya, who went inside the warehouse right away as they split the warehouse. The timing does not work.
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)
Character mistake: Poison Ivy tells her beloved plant "I won't clip off any more of your beautiful petals." She clips off the whole flower, not really "petals." (00:14:35)
Character mistake: The French spoken by the waiter of the cafe is phony in a pretty atrocious way for a supposed high class restaurant. Can't even pronounce "monsieur" right, it's merely a tacked-on accent. (00:04:10)
Other mistake: Batman's lungs have plot armor; he has all the time to put his mask on even after exposure to the gas, and he reacts to it coughing at first. Nobody else in the episode reacts with a cough. (00:07:55)
Character mistake: Batman's computer warns him about the "air born gas emanating from river front district." It's airborne, and riverfront. (00:07:10)
Christmas With the Joker - S1-E38
Other mistake: Robin is trying to change channel but is unsuccessful, because the Joker hijacked all transmissions. Perhaps also because the remote control he has in hand has just one button. (00:04:40)
Character mistake: When Batman uses his magic computer to analyze Langstrom/Man-Bat, lots of lovely gibberish appears on screen, with some notable typos such as "Bat membaaanes", "Sedum Chloride D", "Mammac higi Index Gat harmal nomeaace at padiotion." Your guess is as good as mine for the last one. (00:21:10)
Be A Clown - S1-E11
Character mistake: The magician's name on the poster is "Proscuitto", which is a wrong spelling for Prosciutto (ham). The misspelling is inconsistent throughout the episode; it is wrong the first time Joker shows the poster, then it's fixed at the fun fair and on tv. The font used is also different.
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)
Other mistake: At the beginning of the episode, the truck of the "Gotham Globe" delivers to the newsstand a nice bunch of copies of the newspaper, which naturally bears the name..."Gotham News" (00:01:20)
Other mistake: Gordon has some impressive ceiling fan in his office, since not only one of its blade supports a full-grown adult hanging by the back of the neck to it, but it even keeps working as usual during it. (00:21:30)
Other mistake: The Scarecrow and his goons escape on an airship, which has the control bridge in the gondola under the main structure. Batman reaches the top of the airship, and so does Anthony the goon...but he does it from a trapdoor on the roof of the gondola. There's a whole structure in between he skipped. (00:15:10)
Factual error: It doesn't seem likely Maxie Zeus could've survived being both electrocuted and hitting concrete real hard at least without some serious injuries.
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.