Enter Batgirl, Exit Penguin - S3-E1
Plot hole: When he abducts Alfred, believing him to be a minister, Penguin suffers a peculiar memory lapse. He's encountered Alfred twice before in previous episodes, even kidnapped him once before (knowing full well that he was Bruce Wayne's butler). Yet here, he fails to recognize Alfred at all. (00:12:30)
Enter Batgirl, Exit Penguin - S3-E1
Revealing mistake: The panel that Batgirl makes her entrance through can be plainly seen as a prop mounted on top of the set of stairs she comes down.
Ring Around the Riddler - S3-E2
Continuity mistake: When Batgirl finds Betsy with the huge magnet under the boxing ring Batgirl throws the rope around the lever, then as the rope pulls the lever down the rope slips off and falls, but in the next shot the rope is still up around the lever. (00:21:25)
Continuity mistake: Batgirl's outfit includes boots with kitten heels, but during the fight scenes the stuntwoman's boots have block heels. (00:19:45 - 00:21:25)
The Sport of Penguins (1) - S3-E4
Deliberate mistake: After the episode intro, in the first shot we see the words "The New York Public Library" above the entrance to the library, where Barbara Gordon works. However, it's stated in S3xE1 that she works at Gotham City Library, and even in this episode when Penguin listens to the news about the bomb, it's noted as the Gotham Library. (00:02:00)
A Horse of Another Color (2) - S3-E5
Revealing mistake: Ethel Merman just can't keep a straight face amidst Batman's campy silliness. Here and in the previous episode, she can be seen cracking up in several of her scenes with Burgess Meredith. (00:05:00)
A Horse of Another Color (2) - S3-E5
Visible crew/equipment: The stunt rider doubling Penguin in the horse race is pretty easy to spot. He's younger and thinner (despite an obviously padded costume), and his nose is about two inches shorter. (00:18:00)
The Unkindest Tut of All - S3-E6
Continuity mistake: When the Batmobile pulls up to the theater where Tut's henchmen are emerging, Batman challenges them while standing at the open driver's side door. You can see his left hand closing the door, as well as hear it click shut - but in the next, reverse angle shot, as he and Robin leap into the fray, the car door is standing wide open again. (00:08:00)
The Unkindest Tut of All - S3-E6
Deliberate mistake: When Batman has figured out King Tut's plot to steal ancient Egyptian scrolls from the Gotham City Library, he and Robin rush away, and in the shot of the library exterior, the words "The New York Public Library" is quite noticeable above the entryway. (00:18:00)
Continuity mistake: Lila comes through the bead curtain with the poison lilacs wrapped in green tissue paper. She drops the flowers, and in the next shot of them on the floor, the blooms don't even remotely resemble the ones she was just carrying - and the green paper has disappeared altogether. (00:10:55)
Visible crew/equipment: At the start, Egghead and the Cossacks ride past two women, and they stop to watch, then when the camera zooms in on them the reflection of the moving boom pole/mic is visible on the glass window, at the top right side of the screen.
How to Hatch a Dinosaur (2) - S3-E9
Factual error: Gotham City's museum should brush up on its paleontology. Their sign claims the neosaurus egg is 40 million years old. A) Neosaurus lived in the early Permian period, 290 million years ago. And B) All dinosaurs were rendered extinct 65 million years ago, most likely by an asteroid strike. So 40 million years ago, there were no dinosaurs on Earth. (00:06:50)
How to Hatch a Dinosaur (2) - S3-E9
Continuity mistake: When Barbara delivers the rare book on paleontology to Professor Dactyl, during this scene Dactyl holds the book with its spine either facing toward the right or the spine facing the opposite way, depending on the angle of the shot. (00:07:00)
How to Hatch a Dinosaur (2) - S3-E9
Visible crew/equipment: While Batman and Robin are in Commissioner Gordon's office Barbara reports the theft of the Neosaurus egg, and when Batman suspects it's connected to the radium theft, he and Robin decide to use the Batcomputer at the Batcave. Just as the Dynamic Duo rush to Gordon's door the camera turns to follow them, and we can see filming equipment at the right side of the screen as it tries to move out of view. (00:09:55)
How to Hatch a Dinosaur (2) - S3-E9
Visible crew/equipment: After Egghead tells Olga he's planning a three-course meal for the Neosaurus consisting of Batman, Robin, and Batgirl, and for dessert - Commissioner Gordon and Chief O'Hara. Then it cuts to the Batcave as Batman talks about the Bat-geiger, and when the camera moves closer we can see the camera movement's reflection on the windshield, at the bottom right corner of the screen. (00:15:15)
Surf's Up! Joker's Under! - S3-E10
Other mistake: An amazingly precognizant Dick Grayson is already wearing his surfing togs before Commissioner Gordon calls to say that Joker has invaded the surfing community. (00:04:30)
Suggested correction: Dick isn't amazingly precognizant. He's wearing swim trunks while using the rag to prep his own surfboard. Barbara Gordon was already at the beach with Skip, and Dick is heading to the beach with his surfboard as well (00:04:34).
Surf's Up! Joker's Under! - S3-E10
Visible crew/equipment: After Batman and Robin head out to Joker's hideout, when it cuts to Joker upon his success at stealing all of Skip's talent and vigor, just as Joker says, "You know what this means boys, the surfing championship," we can see the shadow of the boom mic moving at the far right side of the screen. (00:09:50)
Surf's Up! Joker's Under! - S3-E10
Revealing mistake: While Batman and Robin are being processed into the foam surfboard blanks, they are lying on two wood workbenches. When Riptide and Wipeout begin adding the coat of resin to both foam blanks, just as Riptide announces both blanks are smoking, we can see under Robin's wood workbench the fallen wired smoking apparatus used in the stunt. (00:13:05)
Surf's Up! Joker's Under! - S3-E10
Visible crew/equipment: After Batman wins the competition, when Hot Dog is finally released from the trash can Joker rushes over to claim it was just a little joke, and the microphone pops up into view at the bottom of the screen. (00:21:10)
Surf's Up! Joker's Under! - S3-E10
Revealing mistake: When the Dynamic Duo are locked in the board blanks, you see the jets where the smoke and flame come out.