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)
Character mistake: Penguin shouts, "I am not a human being! I am an animal! Cold-blooded!" Penguins are actually warm-blooded.
Continuity mistake: When the Penguin hooks the umbrella on Cat Woman he turns to our left to watch her fly away. A shot later he is facing straight, but a shot later he has suddenly moved 2 meters to the right and is facing the right side.
Continuity mistake: After The Penguin dies Batman's car drives next to a white car with its windshield covered in snow. From the shot inside Batman's car the snow is gone.
Continuity mistake: When the clown lies unconscious there's a string several centimeters behind his head. A shot later his head is on top of the string.
Continuity mistake: When Selina is about to taser the clown she puts on an evil face, but a shot later from a different shot she is staring with a calm look.
Continuity mistake: When Selina watches the clown's hand holding the taser, his fingers are clinched around it. A shot later his index finger is sticking out.
Continuity mistake: When Batman talks with The Penguin, before Catwoman arrives, The Penguin's left arm is raised or not depending on the shot.
Continuity mistake: Catwoman turns the microwave dial to the right, pointing in a 3 o'clock position. A shot later it points in a 12 O'Clock position. (00:56:04)
Continuity mistake: Inside the cage, Max covers his mouth with his hand and then uncovers it and grabs an iron bar. A shot later he is suddenly covering his mouth again. (01:37:16)
Revealing mistake: When The Penguin controls the Batmobile, before it crashes against a car on the left and sends it flying away, check the car's rear wheels: they're not touching the road.
Continuity mistake: While arranging the plan with the clowns, the Penguin throws his clothes on the floor, which change positions between shots. (01:29:23 - 01:31:00)
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.
Continuity mistake: Towards the end when Bruce takes the cat, the wounds on his left cheek change from faded to fresh.
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).