Continuity mistake: As Cat yells, and after the swinging sequence, the kids are dropping their piñata bats. As the camera cuts to a few shots of close ups on the kids, you see no bats in their hands. After the shot widens out, you see the kids drop their bats again.
Continuity mistake: In the scene at the birthday party, when the trio is at the window looking inside a shot shows them turning and yelling. It goes to another zoomed out shot, but they turn a second time.
Continuity mistake: In the scene where Alec Baldwin is in the house to discuss Conrad going to military school he is dressed for work. He puts his briefcase down and sets his sunglasses on top of it. In the next scene the glasses are behind and to the side of the case and in the next scene they are back on top of the case. And so on.
Continuity mistake: When Larry first arrives at the house there is a screen door attached to the front door, which he holds open. In all other scenes the screen door is gone.
Continuity mistake: When Conrad, Sally, and the Cat are jumping up and down on the sofa, on the table next to the sofa, the book next to the lamp keeps changing position. It's close to the lamp, then near the lamp, sideways, longways all during the scene.
Continuity mistake: In the scene, 20 minutes before the end of the movie, where the cat is dancing in a rave, the pretty girl he is dancing with wears her top on her shoulders when seen from the front, but off her shoulders when seen from behind.
Continuity mistake: As Sally, Conrad, and the Cat look in the window of the house at the birthday party, a house next door is reflected. However, when the camera looks out at them, there's no house behind them.
Continuity mistake: After the dog is secured and the kids and Cat are running, at one point Lawrence is only about thirty feet behind them. When they get into one of the kiosks, Lawrence is nowhere near, and so couldn't have known where they went. But a minute later, he's sliding down the pole and pushing through the crowd in the party area after the trio.
Continuity mistake: When the Cat is on the picket fence, during the close ups of him, he has his elbows on the fence. When the camera is on Sally, you can see his right hand on the fence, instead of his elbow.
Continuity mistake: When the Hummer comes out of the garage, it looks normal. When the shot cuts to the kids and then back, look at the back right wheel. You can see the back wheel of the S.L.O.W., and the end of the exhaust pipe.
Continuity mistake: When the Cat goes to "look under the hood", he looks back over his shoulder at the kids after passing gas. You can see the definite line of white on his face that is well short of the hairline. The next time that you see his face, the white goes all the way into the hairline.
Continuity mistake: After the Cat, Sally, and Conrad get into the S.L.O.W., the Cat goes from having no goggles on preparing to leave, to having goggles on when pulling out. For the rest of the S.L.O.W. shots, he has no goggles.
Continuity mistake: When Conrad, Sally and the Cat come out of the bedroom after they have first met, the camera zooms on Sally. The door behind her is closed. Goes to wide shot-Conrad is still walking out the doorway and the door is open. After that, the door remains closed.
Continuity mistake: In the scene where the cat cuts off his tail, when he first hits it with the knife it bounces off but in the next shot it went through.
Continuity mistake: The pipe on the side of the house that Lawrence came out of as the house went back to normal, doesn't exist at any other time in the movie.
Continuity mistake: In the wide shot of the countryside, when Joan and Lawrence are going to Joan's house, you hear the police siren, but you don't see the police vehicle. Suddenly, there are no other cars, and there's the Things posing as motorcycle cops right behind Joan.
Continuity mistake: Towards the end of the FUN song, Cat has a bottle of milk on a silver tray balanced on his foot. When the camera is looking at Sally, the bottle on the tray comes up into view, but now, there's a glass of milk on it that wasn't there before.
Continuity mistake: When Lawrence comes in and sees Conrad and Sally jumping on the couch, he goes into the kitchen to nick all the food. He has a sandwich in this right hand, but after he starts sneezing to leave the house, the sandwich is on the left hand.
Continuity mistake: In the beginning of the movie the polka dots on Joan's dress are big, then when the cat in the hat takes the dress out of the closet to clean the mess on the walls from the cupcake batter exploding from the oven, they're smaller.
Chosen answer: Theodor Seuss Geisel, or Dr. Suess as we know him, published most of his books between the late 1930's and the late 1980's. "The Cat in the Hat" was first published in 1957. Dr. Seuss' works generally tell the stories of fantastical characters in imaginary places, meant to be timeless. Illustrations and animated adaptations show buildings and objects with unusual proportions, odd shapes and bizarre functions. The live action film of "The Cat in the Hat, " however, is rooted to reality by its decidedly human child protagonists in an ordinary house in an ordinary neighborhood. The production design, costume design and set decoration of the 2003 film seem also to have the goal of achieving a certain timelessness. No date reference is given. However, there a decidedly stylized quality of 1950's-1960's suburban architecture and design, complete with its generic forms, chimneys, picket fences, and colors such as yellows and avocado greens, reflecting the common decor of the time. Similar to the 1971 TV short, which seems to provide a reference point for the design aesthetic of the film, nothing appears exceedingly futuristic nor rooted in period styles like victorian or colonial. I have also posed your question to Rita Ryack, the film's costume designer, whom I found on Facebook. If she sees my questions and decides to respond, I will add her insights to this answer.