Revealing mistake: After Catwoman's line "Life's a bitch. Now so am I.", she is thrown onto a diagonal roof by Batman. The roof wobbles uncontrollably as she lands on it. (01:00:30)
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)
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 the Penguin picks up the ointment bottles, he throws them up and they land on the bed and pillows. These bottles and Catwoman's whip, which lays on the center of the bed, keep changing position. (01:02:00)
Continuity mistake: Catwoman looks at the Penguins enemy list, and it is left with the top page flipped up, but when Catwoman puts the bird in her mouth, the page is back to normal. (01:02:30)
Continuity mistake: Catwoman's lipstick smears down onto her chin when she puts The Penguin's bird in her mouth, yet in the shot just before she gives herself a "bath", the lipstick momentarily is gone. (01:03:20)
Audio problem: When Oswald holds Catwoman's cat down to the bed while she puts his bird in her mouth, hisses and meows are heard from the cat, but it doesn't open it's mouth. (01:03:25)
Revealing mistake: In one scene, the Penguin is making a "bat" shadow puppet on the ceiling. But there's no light behind his hands. If there's no light, there's no shadow. (01:03:45)
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: 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 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)
Revealing mistake: When saving the Ice Princess, Catwoman throws a chair at Batman. The chair is clearly broken and damaged, even before it makes contact with Batman. (01:14:10)
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)
Visible crew/equipment: After the policemen shoot Batman, he falls backwards and slides down the circular ledge. When it cuts to a close-up of him dropping on his back to the ground, the hand of the crewmember placing him down to the ground is visible. (01:15:25)
Revealing mistake: On the rooftop, Catwoman digs her claw into Batman's chest, but she clearly just puts her hand flat on his chest and you can clearly see in the first shot no claw is left embedded in his suit. (01:16:25)
Revealing mistake: When Batman dives off the building with his bat-glider, there are two wires visible coming off his shoulders, most easily visible before he reaches the horizontal. (01:16:45)
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 pours Catwoman a glass of champagne, the properties of the bubbles and the actual amount of champagne in Catwoman's glass differs. (01:17:40)
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)
Visible crew/equipment: After Batman and Catwoman's mistletoe banter, a wire can be seen attached to his back as he glides off the rooftop. (01:20:15)
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.