Maid Marilyn, as with many past villain's moles, decided to help Batman by providing him and Robin with swords. However, there is no reason why she decided to do it.
The action titles for this and the subsequent episode are in Old English and include such gems as Zap-eth!!, Thwape!!, and !ox?-eth!!
There appears to be a deleted scene, generating a continuity goof. Batman and Robin are caught in the net, and Batman says that he'll cut them free. The camera immediately cuts away. When Archer and his gang come down a minute later, Batman and Robin are unconscious for no apparent reason.
Look carefully at the balloons in the vacuum chamber and you can see the explosive caps on them.
Without an air hose or some other means of directing the air to his and Robin's mouths, any air from the utility belt would be sucked out of the room as quickly as it was released from the utility belt tank.
Notice during the party fight, Batman calls out to the crowd to stop fighting while his lips are not moving.
This marks the first time that Chief O'Hara rode in the Batmobile.
Only Robin has a cliffhanger here.
When Batman remotely activates the Batmobile's seat to eject the bomb, you can see that the exploding bomb is held by a cable.
Notice in the bridge dedication scene, the fake Commissioner walks to the left side of the bridge. But when he falls off the bridge it is on the right side.
Goof: Look for the string pulling the gurney as Bruce heads for the 300 ft drop sign.
Bruce Wayne has a cliffhanger at the end of this story instead of Robin, who is in the batcave.
Commissioner Gordon reads a report about a giant sphinx, the golden statue (with a human body and a jackal's head) in Gotham City's Central Park. However a sphinx is defined as a feline (generally a lion) with the head of a human, not the other way around.
Notice when Bruce is ready to escape from the ambulance, the interior shot shows what appears to be a set of double doors (hinges at both sides, split down the middle), yet from the outside, it's the standard single rear door that's shown.
Joker's mole was never captured in this episode. She is last seen escaping with Joker from the hideout but was never mentioned or seen again.
As Batman frees Robin, he loudly mentions Aunt Harriet and her nourishing meals. Moth is only a few feet away, and Riddler is within earshot as well, meaning they would have a solid clue to Batman's secret identity.
When Riddler's henchman put Robin on the rack, they stretch his arms tight above his head. However, when Batman enters the museum and casts his silhouette, Robin's elbows are bent at 90 degree angles.
When Batman and Robin escape Riddler's death trap, Batman's Bat-Belt has the typical yellow boxes on it that are roughly the same height as the belt itself. However, when Batman and Robin arrive at the museum, the boxes are much taller and offset unevenly from each other, and thicker than usual. Later, when Batman tries to contact the captured Robin on the Bat-Communicator, the belt is back to its normal dimensions that were originally shown.