Continuity mistake: Catwoman looks at the Penguins enemy list, and it is left with the top page flipped up, but when Catwoman puts the bird in her mouth, the page is back to normal. (01:02:30)
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: When the Penguin shoots the clown henchman for questioning his scheme, the clown's white hair cap flies off. In the next shot, as the Penguin kicks the clown into the water, it is back on his head. (01:29:30)
Continuity mistake: When Selina removes her catwoman mask in front of Max, her hair is suddenly much more messy and tangled in the second shot where she says "Because he *is* Batman you moron." (01:49:05)
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 piece of wall that Batman yanks out of the wall with his gadget is clearly in a much different shape after it has been taken out. (00:15:20)
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: Catwoman's high heels are missing when she jumps on the bouncing-mat in the toy store. (00:53:45)
Continuity mistake: When the Cobblepots throw the pram into the lake, in a wide shot the water surrounding it is rippling and there isn't much snow on the water. In the closeup the water is still and the lake is covered in snowflakes. (00:02:05)
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 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: Batman's large fish tank (which opens the sphinx statue) is not there in the shot where Bruce is sitting in his chair and the Batman symbol is then shone on his bookcase. (00:12:45)
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)
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 Selina enters her apartment after going back to work, there is no wooden spoon in her sink draining rack, but one appears later when she puts the teddies in the sink. (00:29:00 - 00:29:50)
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: The little Bat-Gadget that Batman programs, to knock out the four gang members changes from sailing at head height, to suddenly at about a foot off of the ground between shots, so that the poodle can snatch it. (00:53:00)
Continuity mistake: When Batman is nearing the two clowns juggling flames, the clowns drop their flaming batons twice between shots. (00:13:55)
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).