Revealing mistake: When Batman and Robin are ascending up the side of a building while holding onto a rope, you can see the lines pulling on the bottom of their capes, so that they can give it the effect that Batman and Robin's capes are hanging down in the vertical position. (01:00:00)
Continuity mistake: When the officials are being dehydrated, close ups of the liquid in the dehydrater show the level increasing up to about 75% but far away shots show the level steady at about 20%.
Visible crew/equipment: In the final fight scene on top of the submarine you can see the ripples and shadows on the painted sky backdrop behind the submarine. (01:31:05)
Continuity mistake: Before the final torpedo, the projector lenses are out. After the explosion, the Batboat is gone, and the projector is again concealed. Batman didn't have time to put the cover on.
Continuity mistake: As the Batcopter approaches the yacht, switching between the aerial view and inside the cabin, Batman is seen both standing outside ready to descend the ladder, and piloting.
Visible crew/equipment: As the Bat copter is approaching the yacht, in the frame is a crew member, either a member of the yacht's crew...or production crew. He apparently realises he is on camera and ducks down behind a railing.
Continuity mistake: Toward the end of the fight scene on the deck, knotted ropes suddenly appear.
Revealing mistake: As the camera watches the duel between Batman and Penguin, the wall of the set is painfully obvious, as you can see lines and ripples in the scenery of the sky.
Continuity mistake: After Robin gets rid of a goon, Joker comes toward him. After Joker misses with a swing, Robin pops him and he starts to go overboard. A second later he goes over again.
Revealing mistake: After hitting the Riddler and Joker, a thug with the red and white striped cap goes to hit Batman. As he does, Batman starts to turn away from the oncoming punch well before the man's fist is even near him.
Continuity mistake: When boarding the sub, Robin ties the Batboat off to keep it in place, but it disappears when the fight breaks out. Also, they come aboard well aft of the forward hatch, but a moment later, they're just a couple feet away from it, walking towards the Conning tower.
Continuity mistake: As Joker uses the dehydrator, the amount of water in the container varies between shots from almost empty to almost full and back.
Audio problem: After Guinea Pig 4 disappears, the camera looks at Riddler and Catwoman. You hear Riddler giggling, but he has an astonished look on his face for a second and then giggles.
Visible crew/equipment: As the Batboat preps to leave, the rotor wash of the camera chopper is visible playing across the water, and as it takes off, the blades of the chopper are visible as it tries to catch up to the boat.
Revealing mistake: As the Batmobile approaches the camera on the pier, the tire tracks from a previous take are visible on the deck boards, and as the Batmobile nears, it follows the tracks precisely.
Other mistake: When the shark falls away from the ladder, the hook used to hold it in place is visible.
Visible crew/equipment: When Batman is running to get rid of the bomb, when he runs past some windows you can briefly see the camera and its stand in the reflection. (00:59:55)
Revealing mistake: When Robin is trying to get the sub to surface using Bat Depth Charges, the sub is rocking violently. The rack that contains the vials with the Security Council's dust not only sways back and forth, but lies nearly flat several times, and always at impossible angles. This goes against physics, and gravity. The rack should have fallen off the table more than a few times.
Revealing mistake: Whenever you see the underwater shots of the sub, and the torpedoes, you can see the sides of the pool where the filming was done.
Other mistake: When searching the buoy for clues, Batman goes to take out an obvious screw that was supposed to hold on the panel hiding the projector. The screw is located in the top of a seam where two panels were riveted. After removal, the panel is removed and you can see the seam again that would have been hidden by the panel, as it was tall enough to fit the side from the walkway to the top. Also, the lenses on the projector were obviously fake. Any projector with lenses that badly chipped and faded would have been repaired or replaced. In addition, Batman is supposedly loosening the screw, but was turning the screw to the right, which would be tightening it.
Answer: The Riddler doesn't sing at all. He yells to the henchmen on board, "Prepare to repell boarders!" He does it in a almost musical way, true, but there's no song.
CCARNI