Continuity mistake: Selina dumps her coat, scarf and bag on the sofa seat when she gets home. In another shot the coat and scarf have changed position, and the bag is gone. (00:22:30)
Continuity mistake: After the Penguin bites the male image consultants nose, he has no blood on his chin. In the next shot it is covered in blood. (00:49:45)
Continuity mistake: The position of the cards and notices stuck on Seleia's fridge change, from when she gets the milk out of the fridge when she's normal, to when she goes back to the fridge later, after being pushed from the window. (00:22:30 - 00:28:55)
Visible crew/equipment: After the scene where Selina shocks the clown henchman with the taser, it cuts to the Mayor thanking Batman. As they walk down off of the walkway and continue down the road, if you look on the floor behind Batman you can see black camera tracks on the floor of the raised, bridge walkway. (00:16:15)
Continuity mistake: When Catwoman and Batman are fighting on the roof, there is a big metal ladder attached to the ledge to the side of them, which keeps disappearing. (00:57:15)
Continuity mistake: The position of the manhole cover, in relation to the manhole changes and the snow around it clears. (00:32:55)
Continuity mistake: When Alfred is walking along with his red gift bag, there is a present at the top of the bag which changes position between shots. (00:06:20)
Continuity mistake: When Selina's looking at the files, the filing cabinets behind her have a wide gap between them. In the next shot they're pushed right next to each other. The items on top (medals, ornaments, etc.) also change. (00:25:00)
Trivia: The Christmas ball scene is symbolic: since it is a masquerade party all the guests are in disguise. The only guests who aren't wearing masks are Bruce Wayne and Selina Kyle. This implies that their real personalities are Batman and Catwoman respectively, and that their public persona is the real disguise.
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)
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)
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 Catwoman exits Schreck's she's doing flips without hells. After the explosion, when she climbs the wall heels appear.
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: 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)
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).