Continuity mistake: When Max is talking to Bruce in his office, the pen and the tray with the coffee pot on it move closer between shots, as Max gets up from his chair. (00:43:00)
Continuity mistake: When Max Schrek leads the Penguin over to the image consultants, two women standing behind them suddenly vanish. (00:48:40)
Continuity mistake: Max's big outer coat and his patterned scarf suddenly disappear between shots, when he leads the Penguin over to his image consultants. (00:48:45)
Continuity mistake: When Max leads the Penguin over to the two image consultants, Josh, the male one, reaches back with his right hand for a cigar. In the next shot he's using his left hand. (00:48:45)
Continuity mistake: When the Penguin bites the guy on the nose, while he is talking to Max Shreck afterward the blood on his face is there, then it disappears, then it's there again. (00:49:40)
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: 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: The position of the fish beside the water cooler changes between shots. (00:51:00)
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: In Schreck's department store, when Catwoman is doing her cartwheels, her heels collapse. (00:53:40)
Continuity mistake: Catwoman's high heels are missing when she jumps on the bouncing-mat in the toy store. (00:53:45)
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 Catwoman smashes a glass display case in Schrek's department store, the position of the items on and around the case change between shots. (00:54:25)
Other mistake: The security guard clearly throws his gun out of hand even before Catwoman's whip touches it. (00:54:35)
Revealing mistake: Catwoman breaks into the department store to blow it up. She punches her fingers through a metal access panel to get to the gas lines. Look closely at the panel - the holes are already in place at the exact locations where she punches through, they're just covered with white paint or putty. (00:55:15)
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: 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: 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 Batman fights Catwoman, he hits her to the floor, and the thick handled end of her whip dangles down and touches the ground. In the next shot it is wrapped and tucked in a circle around her chest. (00:57:25)
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).