Deliberate mistake: When the penguin goes into the cemetery, he bumps a tombstone and it moves. Almost certainly a tribute to legendarily poor director Ed Wood, who Tim Burton later directed a biopic of - this exact thing happened in one of his films. (00:39:15)
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.
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.