Revealing mistake: When Batman glides off the rooftop we catch a glimpse of his face as he flies over Gotham. It isn't Michael Keaton, it's a rather crude looking dummy. (01:20:15)
Visible crew/equipment: When the Penguin dies and the penguins slide him into the water you can see the slide-board he was laying on slip out ahead of him under the water. It is also very clear that the penguins aren't even touching him as they pull him into the water. (01:53:00)
Continuity mistake: After Selina pours Max Schrek his coffee in the first boardroom meeting, she walks around his chair twice. (00:07:30)
Revealing mistake: The snow that they use floats on water in almost every scene. (00:02:00)
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)
Continuity mistake: When the Penguin picks up the ointment bottles, he throws them up and they land on the bed and pillows. These bottles and Catwoman's whip, which lays on the center of the bed, keep changing position. (01:02:00)
Revealing mistake: When The Penguin sends his penguin army out into Gotham City, the ripples/waves in the water don't match the position of some of the penguins as they swim towards the exit. (01:43:55)
Continuity mistake: When Catwoman saves the woman from the alleyman, she has high heels on, but after she says "I am Catwoman. Hear me roar." she starts doing backflips, and clearly has flat black shoes on. (00:41:45)
Continuity mistake: When the Penguin is talking to his penguin audience about stealing first, second, third and fourth born children, the penguins chair, box and umbrella stand in the background keep changing position. (01:38:25)
Continuity mistake: Selina grabs some stuffed animals and throws them in the sink, where she starts jamming a monkey down the garborator. We cut to her face, and when we cut back to the sink, all the other stuffed animals are gone, but we know she hasn't had a chance to shred them because she is still shredding the last of the monkey.
Continuity mistake: When Selina is creating her Catwoman suit, the items she tips out from her sewing kit box change formation and position. (00:32:25)
Revealing mistake: After Catwoman's line "Life's a bitch. Now so am I.", she is thrown onto a diagonal roof by Batman. The roof wobbles uncontrollably as she lands on it. (01:00:30)
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 is walking up to Selina from behind, we see her flipping through files, and she puts the paper back down into the drawer. In the very next closeup she's suddenly looking at another file. (00:24:25)
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: When the Penguin goes to visit his parents grave, the umbrella he drops before he walks up to it changes position between shots, alternation from beside / in front of the bush. (00:39:10)
Continuity mistake: After Max Schrek throws some of the presents out to the crowd, when it cuts back, between shots a large green present on the top of the pile vanishes. (00:09:55)
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: During shots, before the shot of the two cats coming through the window and onto the table, the items on the table (lamp, snowglobe, glowing santa, etc.) change positions. (00:30:15)
Continuity mistake: When Selina arrives back home after being pushed out the window, she presses her answering machine button and brings her arm to her side. In the next shot her hand is on the machine again. (00:29:05)
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).