Revealing mistake: When Robin is being pulled underwater by Ivy's plants he surfaces for air and gets pulled under again. It's obvious the film was just rewound. Then when he finaly gets free we see the shot that was rewound was the same shot used when he escapes. Really bad editing. (01:34:50 - 01:36:40)
Continuity mistake: When Robin steps foot into Poison Ivy's lair she is laid out on her flower bed. If you look at the sleeves of her costume, the ends of the sleeves are fringed in a simple leaf like design. Robin spurns Poison Ivy's affections, and an enfuriated Ivy pushes him into the lily pad pool. She is then confronted by Batman, and a soon to arrive Batgirl. Now - look at the huge, obvious, black rubber "thorn" bracelets that suddenly appear on each of her wrists. (01:37:25)
Other mistake: While fighting Mr. Freeze (and Bane) at the Gotham Observatory, Batman, Robin & Batgirl all have batsuits on, with silver bat (or robin) symbols on their chest. But while they are giving Alfred the cure to Stage 1 of McGregor's Syndrome, for some reason they have changed clothes before giving him the cure. Because now (other than the fact that they have all taken off their masks) Robin has on his original robin suit (with the red robin symbol across his chest) and Batgirl has on a gray t-shirt. (01:55:25 - 01:56:15)
Factual error: Why is there a stellar observatory in the middle of a very large city, most of the stars would be drowned out by the city lights to the point of the observatory being useless. Also, the dome is very high up on top of a "building". Such buildings need to flex a little bit in the wind to keep them from breaking, this would make it impossible for the telescope to focus on anything for a timed exposure of film to make those neat pictures of galaxies and such. (00:35:20)
Other mistake: When Mr. Freeze threatens to freeze all of Gotham City, he has a big snowglobe in his hand. He freezes the snowglobe, then shatters it in is hand. When he crushes it open with his hand, the inside of the snowglobe is empty. There is no water, frozen or unfrozen, that comes out of the snowglobe when it breaks. (01:23:50)
Continuity mistake: The first confrontation with Mr. Freeze and his henchman involves them skating around a large ice covered area. The henchman are not using ice skates, but rollerblades. In the same scene we see ice skating blades pop out of Batman and Robin's boots, but when we actually see them skating, they are on rollerblades as well. (00:06:45)
Continuity mistake: In Dr. Woodrue's lab, two thugs carry Antonio Diego over to an experiment table and chain him to it. The thug on Diego's left has a cowboy hat on. However, just as that thug is pulling Diego's mask over Diego's head a few shots later, the thug's cowboy hat is gone. This same thug also disappears from the aerial shots of the lab as Dr. Woodrue is exclaiming over his genius of turning Diego into Bane, a super soldier, with Venom. Later, when Bane breaks free of his restraints, the thug just shows up out of nowhere to try to hold Bane down. (00:16:00)
Continuity mistake: As Batman, Robin and Batgirl are heading to the Gotham Observatory to confront Mr. Freeze in their new Bat-Vehicles, a Frostbite piloting Mr. Freeze's Freezemobile meets them, crashing into two cars blocking the Freezemobile's way. The two cars the Freezemobile crashed into are gone in a later aerial shot of the Freezemobile having its freeze ray reflected back at it by Batman's shield.