The Puzzles Are Coming (1) - S2-E31
Visible crew/equipment: At the Knab Aircraft hangar Puzzler arrives in the truck just as Knab is leaving, and when Puzzler walks to the back of the truck the reflection of the boom mic is visible on the right back door windows. (00:14:45)
The Bat's Kow Tow (2) - S2-E30
Visible crew/equipment: While Allan Stevens interviews Batman and Robin they have surprise visitors, and as Catwoman and her Kittens take their places pointing the weapons at the audience, the black tape mark is visible on the floor at Catwoman's feet. (00:06:45)
It's the Way You Play the Game (2) - S2-E26
Visible crew/equipment: After Batman and Robin have "set another youth on the road to a brighter tomorrow," they walk away from Andy, then when they stand beside the Batmobile, the vertical reflection of the moving boom pole/mic is visible right beside Robin's reflection, on the left side of the windshield. (00:03:50)
Revealing mistake: After Shame and his baddies steal Bruce's limo. Bruce shows Dick and Alfred that he had the remote control unit keep the Bat-cycle (with Alf-cycle) following them at a safe distance. In the shots facing the Bat-cycle, attached to the front wheel there's a rope pulling it. (00:17:05)
Marsha, Queen of Diamonds (1) - S2-E23
Continuity mistake: After Batman has been hit by Marsha's love dart, when Robin pulls the dart out and then begs Batman to resist it, in these semi closeups note Burt Ward's uncovered forearm with his still-healing burn wound. Then, while the Dynamic Duo fight Marsha's sabre wielding goons, Marsha hits Robin with another one of her darts and orders him to attack Batman. When this happens, Burt Ward's forearm now has a compression bandage around the wound. (00:13:55)
The Joker's Provokers (2) - S2-E22
Continuity mistake: While Joker and his baddies are in the vent shaft at the waterworks, Joker takes out the envelope and holds the envelope with his left palm up, but in the closeup his left palm is down as he pours the pills into his right hand. (00:14:50)
The Yegg Foes in Gotham (2) - S2-E14
Visible crew/equipment: After Bruce defeats the radar egg using a grape it cuts to Commissioner Gordon at the raccoon pellet ceremony, and when the millionaires walk in, there are two chalk T-marks visible on the floor, beside Chief Screaming Chicken.
The Clock King's Crazy Crimes (1) - S2-E11
Visible crew/equipment: After the Dynamic Duo climb up the side of the building they enter through the window, and a chalk T-mark is visible on the floor where Batman stops when he sees Clock King sitting at a desk. Then, as Batman and Robin slide around on the floor coated with watch oil, when Clock King stands up we can also see the curved chalk mark on the floor by his feet. (00:21:50)
The Clock King's Crazy Crimes (1) - S2-E11
Continuity mistake: When Clock King steals his favorite painting from the gallery, as he places it through the wall hole note the strips of tape adhered to the paintings back, and its hanging wire near the bottom (it's upside down). In the next shot from the other side of the wall hole, the painting is now turned the opposite way (it's right side up), note the tape strips. (00:16:25)
Tut's Case is Shut (2) - S2-E8
Revealing mistake: While Chief O'Hara is outside on the ledge of the top floor, King Tut commands him to use the flagpole to do acrobatics. When O'Hara obeys Tut, the vertical wire at the end of the flagpole is visible. (00:08:20)
Visible crew/equipment: While Batman and Robin are tied to the spit and rotating, when Batman says, "If we could just shake this turn spit pole loose," in the next shot note the shadow of a crew member moving their arm up, at the lower right corner of the screen. (00:03:35)
Walk the Straight and Narrow (2) - S2-E2
Visible crew/equipment: At stately Wayne Manor, when Bruce and Dick are practicing their archery, two white tape marks are visible on the grass; one for Dick and the other for Alfred. (00:23:05)
Walk the Straight and Narrow (2) - S2-E2
Visible crew/equipment: After Archer and his goons have hit the armored truck, when the security guard pulls out the bag of money from the back of the truck and shows it to his partner, the chalk T-mark is visible on the ground between their feet. (00:10:20)
Walk the Straight and Narrow (2) - S2-E2
Revealing mistake: When the armored truck with the ten million is hit, during this scene we can see stunt wires for some of the arrows used by Archer and his goons. (00:09:00)
Walk the Straight and Narrow (2) - S2-E2
Revealing mistake: At the start, while Archer and his goons are riding toward Batman and Robin who are tied to the stakes, when the Dynamic Duo use their Bat-springs the stunt wires lifting them are visible. (00:03:05)
Shoot a Crooked Arrow (1) - S2-E1
Revealing mistake: In Commissioner Gordon's office, just as Gordon tells Dale that with Batman and Robin on their side no harm will befall the money, the top of the set is visible at the top right corner of the screen. (00:06:25)
Shoot a Crooked Arrow (1) - S2-E1
Revealing mistake: At Archer's underground hideout, Batman and Robin are strung up by their thumbs, but in fact the stunt wires that lead to their cloaked backs are visible. (00:21:40)
Continuity mistake: During the fight, the desk mat and desk calendar are moved initially and then moved again later in the fight. (00:19:03 - 00:22:00)
The Bird's Last Jest (2) - S2-E28
Continuity mistake: When the Dynamic Duo goes up the Bat Pole chute, the NEGATE COSTUME CHANGE lever is down. When they come down as Dick and Bruce, the lever is up, and Robin pulls it down to stop the instant change back to Dick and Bruce.
The Clock King's Crazy Crimes (1) - S2-E11
Continuity mistake: After starting the sand in the giant hourglass, Clock King puts on his alarm clock top hat. Between distance and close shots, the clock reads a few minutes to three, then Three o'clock in the closeups.
Answer: There wasn't one singular city used. It was shot in and around various locations in California, plus on a lot of sets and backlots. Ex. Some scenes were shot in LA, some in Pasadena, some in Santa Barbara, etc.
TedStixon