Continuity mistake: When Oswald goes upstairs and finds Catwoman on his bed, he goes over and hangs his hat over the end of an umbrella in the rack. When he picks up an umbrella as he talks with Catwoman, the hat is now in a different position. (01:01:30 - 01:02:00)
Continuity mistake: When Batman is fighting some goons right before his boomerang is stolen by a poodle, one of the goons attacks him with a metal pipe, which both opponents take hold of in one shot. Batman then delivers a blow to the assailant, the view shifts further away, and we can see that neither Batman or the goon have the pipe, and it is nowhere on the ground nearby. After this, Batman turns to his right to defend against another goon and we see another enemy coming at him from behind, but after the view shifts to another shot and then back to Batman, this enemy is nowhere to be found.
Continuity mistake: When Max Schrek leads the Penguin over to the image consultants, two women standing behind them suddenly vanish. (00:48:40)
Continuity mistake: When Batman is on the roof, his cape becomes a glider, the glider is separate from his cape as his cape falls off behind him. When he floats down the glider cape once again resembles his regular cape. (01:16:45)
Continuity mistake: When The Penguin is explaining his scheme about stealing the children fron their cribs and sending them to their watery graves, a black line of spit runs down his chin. When he turns around it's gone. (01:29:15)
Continuity mistake: When the penguin is at his parents grave, as he kneels, between shots the roses he holds change completely. In one shot one of the roses has a leaf on the stem, right under the rosebud. In the next shot the leaf has vanished. (00:39:20)
Continuity mistake: In the shot of Mr. and Mrs. Cobblepot by the window, they both hold a martini. Mr. Cobblepot's martini glass is full to the top. But after the baby pulls the cat into his crib, Mr. C's martini glass is suddenly only a quarter full. (00:00:50)
Continuity mistake: When the baby basket is floating through the sewers, there are shadows but no lights, except for one scene where the lights are under water.
Continuity mistake: When Selina is listening to her answering machine in her apartment, the items on the pull-out drawer, under the shelf with the fishbowl on it, change and move around between shots. (00:22:55)
Continuity mistake: When Alfred is drving Bruce in the car at the end of the film, the same car can be seen parked on the street, in different places, from different angles, about five or six times. (01:53:25)
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)
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)
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.