Continuity mistake: When Catwoman pulls Max Schrek up out of the water, Max's hair is very wet, and is stuck down flat on his forehead. In the very next shot it is much drier and is wavier and stringy. (01:46:40)
Continuity mistake: When The Penguin starts to shoot at the booing crowd from his umbrella, the same microphone, on the far left, falls from the podium twice in different shots. (01:27:15)
Continuity mistake: When Batman and Catwoman fight in front of the Ice Princess, Catwoman's black whip hangs from the ceiling. As she does backflips over to the Ice Princess, the whip vanishes for a shot. (01:14:00)
Continuity mistake: When Batman pulls the gag cloth from the Ice Princess' mouth, we see a reverse shot, with the Ice Princess' back totally bare. In the next shot two strips of cloth hang down her back. (01:13:40)
Continuity mistake: When Batman spots the Ice Princess tied up, he shoots his glider and the tip lands in a rough stone wall, but in the next shot as he glides down along the wire, the tip is embedded in a rusty metal wall. (01:13:10)
Continuity mistake: The kettles on the oven hobs in Selina's apartment change their position and they change which hob they are on as well between the shots of Selina entering her apartment, and her grabbing the frying pan. (00:28:40)
Continuity mistake: When Selina is wrecking her apartment, she grabs a frying pan and throws it at a small display case, smashing all the glass and ornaments. Between shots the glass/ornaments on the case shelves differs. (00:30:10)
Continuity mistake: The positions of the cats on Selina's table changes instantly between shots. They swap places and are suddenly doing different things. (00:30:20)
Continuity mistake: When Alfred is walking off of the pavement, and across the grate, we see the penguins hands sticking out of the sewer bars. Then it shows another shot of Alfred looking at the bars, only the snow around and under the bars has changed. (00:06:40)
Visible crew/equipment: When the monkey jumps onto the cage in which Max Schrek is prisoner, you can see a cable clipped to its jacket it is wearing. (01:46:00)
Continuity mistake: When The Penguin shouts "I am not a human being..." he throws his black coat and shirt to the floor. His coat lays in front of him, but in the next shot it is behind him. His shirt also changes position. (01:28:40)
Continuity mistake: As the Ice Princess falls down from the skyscraper, it is clear she will not land on the lighting button, but she does. Between shots the lighting button moves closer to the edge of the stage too. (01:15:10)
Continuity mistake: When Selina arrives home from work, she walks around and listens to her answering machine. She then has to run off to work. When she gets back from work a second time, the dishes and cups in the draining tray beside her sink have totally changed. (00:22:45 - 00:28:45)
Continuity mistake: After Batman pulls the wires from the batmobile roof, the wires disappear/reappear during the scene. (01:20:30)
Continuity mistake: As the Penguin is walking down the steps toward the podium, before Batman plays the messages the Penguin said, a man and a woman standing to the left of the podium swap places between shots. (01:23:30)
Continuity mistake: When Bruce goes to gear up to rescue the Ice Princess, there are visible footprints on the drawbridge that leads into the chamber where all the bat suits are kept. When he then steps back out in his Batman attire, the drawbridge is now clean of all prints. (00:00:24)
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.
Continuity mistake: When the circus gang first attacks, after Batman uses his Batmobile to take out of the two juggling guys on stilts, he opens this flat panel on the passenger side of the Batmobile to take out one of the skull mask wearing bikers. Before taking out of the second biker, he opens that same panel again.
Continuity mistake: The Penguin is getting vegetables thrown at him after Batman jams his speech on the steps. In certain angles he is closer to the banners behind him, while further in others.
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.