Continuity mistake: In the scene where Catwoman and Batman fight each other you can see Catwoman's boots change several times from high heels to flat heels.
Visible crew/equipment: After the scene where Selina shocks the clown henchman with the taser, it cuts to the Mayor thanking Batman. As they walk down off of the walkway and continue down the road, if you look on the floor behind Batman you can see black camera tracks on the floor of the raised, bridge walkway. (00:16:15)
Continuity mistake: When the Penguin shoots the clown henchman for questioning his scheme, the clown's white hair cap flies off. In the next shot, as the Penguin kicks the clown into the water, it is back on his head. (01:29:30)
Continuity mistake: When Selina removes her catwoman mask in front of Max, her hair is suddenly much more messy and tangled in the second shot where she says "Because he *is* Batman you moron." (01:49:05)
Continuity mistake: When Catwoman and Batman are fighting on the roof, there is a big metal ladder attached to the ledge to the side of them, which keeps disappearing. (00:57:15)
Continuity mistake: The piece of wall that Batman yanks out of the wall with his gadget is clearly in a much different shape after it has been taken out. (00:15:20)
Continuity mistake: The position of the manhole cover, in relation to the manhole changes and the snow around it clears. (00:32:55)
Continuity mistake: Catwoman's high heels are missing when she jumps on the bouncing-mat in the toy store. (00:53:45)
Revealing mistake: When The Penguin is controlling the Batmobile, in one shot Batman taps the speedometer and the whole dashboard clearly wobbles back and forth, as it were made of rubber. (01:19:55)
Continuity mistake: When the Cobblepots throw the pram into the lake, in a wide shot the water surrounding it is rippling and there isn't much snow on the water. In the closeup the water is still and the lake is covered in snowflakes. (00:02:05)
Audio problem: When Selina is pushed from to window, her scream doesn't match her mouth movement. (00:27:05)
Continuity mistake: Just after Bruce has spoken to Alfred about him letting Vicky Vale into the Batcave in the past, we see him pulling his jacket on from behind. He puts his right arm in, then starts to reach behind himself to get his left arm in. The shot then cuts to seeing him from the front, and we see him reach behind himself again.
Continuity mistake: When Alfred is walking along with his red gift bag, there is a present at the top of the bag which changes position between shots. (00:06:20)
Continuity mistake: Batman's large fish tank (which opens the sphinx statue) is not there in the shot where Bruce is sitting in his chair and the Batman symbol is then shone on his bookcase. (00:12:45)
Continuity mistake: When Selina's looking at the files, the filing cabinets behind her have a wide gap between them. In the next shot they're pushed right next to each other. The items on top (medals, ornaments, etc.) also change. (00:25:00)
Continuity mistake: When the circus and Batman first make their appearance, one of the circus men grabs Selina Kyle and threatens Batman with a Stun Gun. After the man is knocked unconscious, Selina "zaps" the man. I don't know how many of your are familiar with stun guns but when they are activated on someone or something they don't spark or make a sound. The sound is only heard if held up in the air and is not in contact with anything. Yet when she zaps the man, there is a clear shocking sound.
Continuity mistake: When Selina enters her apartment after going back to work, there is no wooden spoon in her sink draining rack, but one appears later when she puts the teddies in the sink. (00:29:00 - 00:29:50)
Visible crew/equipment: After Selina tasers the henchman, it cuts to the Mayor thanking Batman. As the camera pans past Batman, a noticeable shadow is cast on him. (00:16:15)
Continuity mistake: When there's an overhead shot of the crowd in front of the Hall of Records, there is a person in bright red clothing amidst the people near the doors, pushing against a police officer, but in the next shot when Shreck is speaking to the press, the person is nowhere to be found and could not have exited the crowd in that short time.
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.