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: 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.
Continuity mistake: Towards the end when Bruce takes the cat, the wounds on his left cheek change from faded to fresh.
Revealing mistake: When the penguins emerge to carry the Penguin (character) to the water after he dies, the penguins are blatantly little people in costumes. Their "skin" crinckles unnaturally, and the spot where their arms meet their bodies is very flat and fake-looking.
Revealing mistake: When Batman is driving the Bat-boat, just after he dodges the two rockets the penguins launch at him, as the Bat-boat slams back down into the water in the background, the scale of the water-splash reveal that this effect was achieved using a miniature set and miniature Bat-boat model. The scale of the water splash, and the enormous "drops" that splash up give the effect away.
Continuity mistake: When Selina arrives home at her apartment, she is wearing a brown suit, and then rushes back to work. When Max finds her looking at the files, she is wearing a gray suit with a shawl.
Continuity mistake: In the opening, Penguin's parents look at the cage holding him. From the outside, his shaking is making the cage move slightly side to side. From inside, his shaking is not moving the cage at all.
Revealing mistake: There is a shot of Batman driving the Batmobile around town late at night looking for The Penguin. In this shot, look at the cars parked at the side of the road. They are miniatures as well as the rest of the shot.
Revealing mistake: When the penguins launch the rockets/missiles in the end, watch carefully. In the second wideshot of the rockets launching (right after the bats begin to attack Danny DeVito), you can see two of the rockets hanging in midair, not moving. At the beginning of the shot, you can even see one of them spurting some fire. The rockets (attached to visible guided wires by the effects crew) got stuck in mid air right before the shot began, a few seconds before this second volley of rockets fire off.
Revealing mistake: When The Penguin (character) is first introduced, feeding the other (real) penguins, watch closely. While some of the penguins are real, it's blatantly obvious that some of them (particularly the ones to the left of the screen when Penguin says "Hi") are animatronic puppets, as they have very unnatural neck movements and don't waddle around like the rest. A few shots later, when Penguin says, "I believe the word you're looking for is...", you can even see an animatronic penguin on the left side of the screen that is unnaturally leaning slightly forward, yet never falls, revealing it's a puppet that was mounted to the ground.
Continuity mistake: When Oswald Cobblepot is in his crib as a baby, in outside shots the rubber duck on the string is swaying back and forth. In shots through the crib bars, it is dead still. (00:01:00)
Answer: The film keeps it ambiguous. There are two ways to look at it. Scenario A- She literally died and is brought back to life by the alley-cats somehow, adapting some of their traits. Or... Scenario B- The trauma of falling and sustaining a head-injury, along with her paranoia after Schreck tried to kill her, has driven her mad, and she uses her connection with cats to build a new persona. (Which is supported by the fact that all the things she claims "kills" her with each of her "nine lives" wouldn't actually have killed her. Ex. Her one fall is broken by the kitty-litter truck. Max doesn't hit her in any vital organs when he shoots her. Etc.) Her destroying her apartment is her lashing out at all the things she used to hold dear- her vision of a normal life, etc. It's symbolic of her purging the past and embracing the future. (Plus, oftentimes when people throw fits, they'll smash stuff up).