Revealing mistake: When The Penguin shoots the clown who says "Killing sleeping children...", as the clown falls back to the floor, you can clearly see he falls on a wrinkled, soft mat which has unsuccessfully tried to be disguised. (01:29:30)
Visible crew/equipment: When the Penguin dies and the penguins slide him into the water you can see the slide-board he was laying on slip out ahead of him under the water. It is also very clear that the penguins aren't even touching him as they pull him into the water. (01:53:00)
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: 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: Inside the cage, Max covers his mouth with his hand and then uncovers it and grabs an iron bar. A shot later he is suddenly covering his mouth again. (01:37:16)
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.