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.
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 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 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.
Continuity mistake: When Penguin removes the manhole cover above him right before the Mayor's baby is stolen, he places it right next to the edge of the manhole, but when the baby snatcher jumps in, it is further away.
Continuity mistake: When Selina electrocutes Max while kissing him his head is tilted to the right. Shot changes and it's straight.
Continuity mistake: At the point where the Penguin controls Batman's car from his trailer, we see shots from the inside and outside of his trailer. The Penguin rides the mini-Batmobile in his trailer like crazy, therefore the trailer shakes like hell from the outside, however, the shots inside show ONLY the mini-Batmobile shaking, the floor and trailer seem rock-solid.
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 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 Catwoman exits Schreck's she's doing flips without hells. After the explosion, when she climbs the wall heels appear.
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: 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.
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: 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.
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).