Other mistake: The security guard clearly throws his gun out of hand even before Catwoman's whip touches it. (00:54:35)
Other mistake: When the Penguin is talking on the staircase to his audience of voters, he gives a badge to one young woman. As he lifts it up it is clearly a pin-on design button, however the Penguin leans forward as presses the badge against her blouse as if it were a stick-on design. The badge then stays on the blouse and doesn't fall. (01:00:30)
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.
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.