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.
After escaping Riddler's death trap, Batman calls Commissioner Gordon on the hot line, and Gordon takes the call on the customary red phone. Despite that, Gordon asks who is calling.
Linda Gaye Scott is the heiress to the Scott paper company.
If you look closely at Moth's outfit, it resembles a prototype outfit of what Batgirl would wear in the third season.
The Batcycle is several hundred feet away when Dove and Eagle-Eye spot The Dynamic Duo coming and Eagle-Eye says in a normal tone of voice that he's seeing ghosts. Somehow Robin hears him despite the distance when he jumps out to punch them.