Other mistake: While signing the contract, when Conrad is supposed to "sniff this", he moves to his position a second before the Cat says his line and bobs Conrad's head down.
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.