When Jennifer and David are fighting over the remote control before the Pleasantville Marathon starts at 6:30, they momentarily go to the Prevue Channel. The time shown on that channel is 1:16, not 6:30.
Jack Jones is among the singers included on a list of approved music for the town. In 1958, Jones was still an unknown. He didn't make his recording debut until 1959 and didn't achieve widespread recognition until 1962, when "Lollipops and Roses" hit the charts.
The Dave Brubeck Quartet track, Take 5, (which is played during the diner scene where Bud is asked how he knew about fire) was released in 1959. The next track that is played is Miles Davis's So What was recorded in 1959 a year after the action is meant to be taking place.
The flag outside the school has 48 stars, the correct number for 1958. The one atop the fire truck has 50 stars. By 1958, it was well known that the 50-star flag would be introduced soon, and 50-star flags were available, but it still seems unlikely that an official vehicle would be flying an unofficial flag (especially since the official flag in 1959 had 48 stars until July 3rd, and 49 stars from July 4th until the end of the year).
When a rock is thrown through the window of the soda shop, it goes through the face of the woman in the painting. A moment later, another item is thrown, also breaking the window in a different place, but the woman's face is intact again.
On their way to school on the first day, Jennifer/Mary Sue gets angry and pulls her hair clips out - just before Skip pulls up in his car. After Skip drives away her hair is suddenly clipped back again.
When Bud is about to go to work for the first time, Mary Sue complains to him about having to wear falsies on her date. When she's talking to her date at the restaurant, the falsies are gone. She's wearing them again right after her date is over and she walks into the house.
When the soda shop is wrecked and it is discovered that the juke box still works one of the boys unplugs it after Buddy Holly's "Rave On" starts. When Bud says it's okay and plugs the juke box back in the song starts again, which would not have happened with a circa 1958 juke box. It would have started up where the needle was left by the unplugging.
The TV repairman leaves right before the beginning of the marathon and is seen smiling in his van, looking back at the house. The same shot is seen again at the end of the movie, despite the narrator of the marathon indicating the end of its first hour. It is unlikely the repairman would have simply sat there for a whole hour.
In the bowling alley sequence, the scene begins with two or three 7-10 splits being picked up. Later in the same scene when the mayor is speaking with the scores behind him there are no 8 pin spares listed, only 9 pin spares.
When Bud pulls up in the fire truck to put out the tree fire, he pulls a charged hose from the back of the truck. Hoses in the back of an engine are not connected to the engine's pump, and water would not flow until the pump was engaged.
When the TV repairman talks to David and Jennifer from the television after they've just been transported to Pleasantville, behind him, the test pattern's position on the screen is slightly different in the close-ups. This was done deliberately "to indicate Knott's changing attitudes towards Bud and Mary Sue".
At the very end of the movie, George Parker and Betty Parker are sitting on a bench. The camera pans from George to Betty, then back to where George was sitting, and he "turns into" Mr. Johnson. If you look at Betty before the camera goes back to Mr. Johnson, you can see her bounce. This is from Mr. Johnson sitting down in George's place.