Continuity mistake: The position of the fish beside the water cooler changes between shots. (00:51:00)
Continuity mistake: At Wayne Manor, Bruce receives the projected bat signal while in his study. As he stands up, the circle of light hits only the last shelf on the bookshelf behind Bruce. But in the next shot, the light circle is much lower and hits almost the entire bookshelf. (00:13:10)
Continuity mistake: When the cats are bringing Selina back to life in the alley, the paw prints they make in the snow around her body are subsequently there / gone. It is not snowing, so fresh snow could not make them vanish. (00:27:35)
Continuity mistake: Catwoman is about to land a kick in Batman's face, but from a side angle it hits him square in the chest. (00:57:20)
Continuity mistake: When Catwoman gives Max Schrek the taser-gun kiss, the black wire above them falls down at least four times. (01:50:20)
Continuity mistake: When Selina electrocutes Max while kissing him his head is tilted to the right. Shot changes and it's straight.
Continuity mistake: The fruit and vegetables (tomatoes, lettuces, eggs etc.) thrown at Oswald at his speech, litter the stage as well. The amount and position of these items laying all over the stage changes between shots. (01:27:10)
Continuity mistake: As Oswald and Max talk beside the water cooler, the shape, size and prominence of the blood on Oswald's shirt, beside his black scarf, changes a few times. (00:49:45)
Continuity mistake: When Catwoman is electrocuting Max, when you see a view of the explosion from above, you can see Max walk off the set through the explosion. It is definitely him, not Catwoman!!! (check the clothing.) (01:50:30)
Continuity mistake: When Oswald starts shooting bullets out of his umbrella at his failed mayor speech, the crowd ducks down on the stairs, at the edge of the red stage, laying down their campaign signs. In the next shot some of the crowd and signs have vanished from around the stage, then reappear in the next shot. (01:27:15)
Continuity mistake: Batman is monitoring the progress of the rocket-laden penguins via radar. At every screen refresh, about one per second, the penguins have moved about half a street, way too fast for the way they waddle. (01:42:25)
Continuity mistake: During the scene in Schrek's department store, Catwoman has a tail clipped onto her beltline which keeps disappearing. It is visible when she jumps from the trampoline, and smashes open the door to the gas, but is missing in all the other shots. (00:54:00)
Continuity mistake: When Selina is pouring Max his coffee, the kettle spout changes position. (00:07:20)
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: In the scene where the Batmobile diagnostics detects a foreign object, it shows it being located approximately to the front-left of the windshield. It is also a 2D plan view. Yet Batman automatically knows it is BELOW the car and punches through the floor directly beneath him, which is nowhere near where the Batmobile detects it. (01:21:35)
Continuity mistake: Just after Selina has hit the ground, we see a shot from above, with her lying seemingly dead in the snow. In the next shot the pattern of the snow around her is completely different. (00:27:15)
Continuity mistake: When Selina puts the pink teddy down the shredder, it begins to spit and churn out stuffing and feathers. However in the next shot of Selina grabbing the frying pan, the shredding of the teddy has mysteriously stopped. (00:30:00)
Continuity mistake: When the penguin is going through the birth certificates in the library, he finds a certificate and begins to write. The name of the baby on the certificate is 'Peter Lindsey' but the penguin writes down 'Matthew Gruen.' (00:36:15)
Continuity mistake: The length of the bar which comes out of the side of the batmobile, which subsequently knocks over the clown twirling the batons, changes between shots. (00:13:50)
Continuity mistake: When Oswald is in The Hall of Records, it is snowing heavily. In the next shot of Batman coming around the corner in his batmobile, it isn't snowing. In all following shots it's snowing heavily again. (00:37:55)
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).