Visible crew/equipment: A wire can be seen attached to Oswald Cobblepot as his penguins slide him into the water after he dies.
Continuity mistake: When Selina electrocutes Max while kissing him his head is tilted to the right. Shot changes and it's straight.
Revealing mistake: During the climax, when a rocket hits the "Arctic World" sign and explodes, subsequently causing the polar-bear statue to fall, look closely. The scale of the fire and smoke (particularly the smoke, which looks similar to cigarette-smoke size and not the enormous plumes that such an explosion would create), in addition to the unnatural movements of the alleged large "statue" reveal that this effect was achieved with a rather obvious miniature set.
Audio problem: When the mayor's baby is first stolen, the audience gasps in a very fake way. When the Penguin reveals his plan to steal the first-born sons to the party members later in the movie, they gasp the exact same sound effect. They actually do it a third time, later in Penguin's speech, but it's very quiet.
Continuity mistake: At the point where the Penguin controls Batman's car from his trailer, we see shots from the inside and outside of his trailer. The Penguin rides the mini-Batmobile in his trailer like crazy, therefore the trailer shakes like hell from the outside, however, the shots inside show ONLY the mini-Batmobile shaking, the floor and trailer seem rock-solid.
Continuity mistake: When Batman is fighting some goons right before his boomerang is stolen by a poodle, one of the goons attacks him with a metal pipe, which both opponents take hold of in one shot. Batman then delivers a blow to the assailant, the view shifts further away, and we can see that neither Batman or the goon have the pipe, and it is nowhere on the ground nearby. After this, Batman turns to his right to defend against another goon and we see another enemy coming at him from behind, but after the view shifts to another shot and then back to Batman, this enemy is nowhere to be found.
Continuity mistake: When the baby basket is floating through the sewers, there are shadows but no lights, except for one scene where the lights are under water.
Other mistake: At the end as Penguin is dying after coming up out of the water, blue/black "blood" is coming from his mouth. However the cuts and bruises on his face have red blood coming from them, indicating the inconsistency of what color blood he should be bleeding.
Character mistake: Penguin shouts, "I am not a human being! I am an animal! Cold-blooded!" Penguins are actually warm-blooded.
Deliberate mistake: After Batman destroys The Penguin's controlling system and breaks the TV screen he is 4 meters away from a narrow alley. Shot changes and he's now downtown driving around the city, Then there's a POV shot of him driving towards the narrow alley again, though he is now many meters behind. Then back to shots of him driving downtown until he finally arrives at the narrow alley. It adds up for pace, but it's very awkward indeed.
Continuity mistake: When Catwoman exits Schreck's she's doing flips without hells. After the explosion, when she climbs the wall heels appear.
Continuity mistake: When the Penguin hooks the umbrella on Cat Woman he turns to our left to watch her fly away. A shot later he is facing straight, but a shot later he has suddenly moved 2 meters to the right and is facing the right side.
Continuity mistake: After The Penguin dies Batman's car drives next to a white car with its windshield covered in snow. From the shot inside Batman's car the snow is gone.
Continuity mistake: When the clown lies unconscious there's a string several centimeters behind his head. A shot later his head is on top of the string.
Continuity mistake: When Selina is about to taser the clown she puts on an evil face, but a shot later from a different shot she is staring with a calm look.
Continuity mistake: When Selina watches the clown's hand holding the taser, his fingers are clinched around it. A shot later his index finger is sticking out.
Continuity mistake: When Batman talks with The Penguin, before Catwoman arrives, The Penguin's left arm is raised or not depending on the shot.
Revealing mistake: When The Penguin controls the Batmobile, before it crashes against a car on the left and sends it flying away, check the car's rear wheels: they're not touching the road.
Continuity mistake: After dumping out the sewing kit, Selena picks up a pair of scissors with blue handles. When the camera is in a closeup of her, the scissors have pink handles.
Character mistake: Bruce Wayne talking to Selina Kyle says that Batman probably saved millions of dollars in property damage alone. When Batman first saw Catwoman he didn't do anything to prevent the property damage before the explosion that she caused.
Answer: Nothing was stopping them. After Penguin's true nature was revealed, they most likely started searching the entire sewer system but couldn't find where his lair actually was so they had no choice but to give up.