Continuity mistake: When Miss White is writing Mrs. Heimer on the chalk board, the camera shows Kevin/the class, when the camera comes back to her, she has a different sweater, hairstyle, and her name is written in a different spot. I'm not sure if this is some kind of flash to when everyone comes back to school after summer, or an error.
Continuity mistake: In episode 2.9, in the last scene we can see that Paul still does not play basketball well in the future, and future Kevin narrates that it is so. However, in episode 4.8, Paul actually becomes a better basketball player and makes the basketball team, which means that in the future he would not actually play in the same way or as badly as he did when he was younger.
Continuity mistake: In episode 37, "The St. Valentines Day Massacre", the writing on the card Kevin makes for Winnie changes from the time he makes it to when it's shown again at the end of the episode; he's shown printing it and writing just in one corner of the card, but when the card is shown again, the writing is in cursive and is spread down the side of the card.
Factual error: Kevin and Wayne's bedroom shows a Beatles poster of the White Album. However this album, and presumably the poster as well, didn't come out until November 1968. This season opens with the summer and start of the school year 1968.
Factual error: Paul and Kevin go to the book store to buy "Everything you always wanted to know about sex." In this episode it was still 1968 but the book was not released until 1969.
Continuity mistake: When the gym teacher is drawing on the chalkboard, the kids ask him to draw the whole woman. He does, and the word "ovaries" that he had written disappears. It reappears differently in a second cut.
Other mistake: During the 3-nightmare sequences, there are 25 students, with all desks full. However, 1 desk should have been left open as Kevin appears in the dreams, meaning there should only be 24 students.
Factual error: During the scene when the Doors' "Riders on the Storm" is playing. This scene takes place in late 1968, early 1969. "Riders on the Storm" would not be written for at least another year, and the Doors album with that song was released in early 1971.
Visible crew/equipment: When the boys are picking teams for basketball, a boom mic can be seen in the top left corner of the screen. (00:06:20)
Visible crew/equipment: When Kevin goes into the council room and sees Paul, a boom mic can be seen at the top right corner of the screen. (00:02:20)
Visible crew/equipment: When Paul and Kevin happen upon Eddie and Whinnie in the halls, a boom mic can be seen at the top left of the screen for a split second. (00:09:30)
How I'm Spending My Summer Vacation - S2-E17
Plot hole: When Kevin is upset about Paul leaving for summer and is just lounging around the house, he asks why they can't go on vacation. His mom says "Maybe next Summer." In the very next episode, which takes place in the same Summer, they are going on a "traditional" Summer vacation.
Visible crew/equipment: The reflection of a large light used to light the shot is visible in the car window as Wayne is driving away after dropping Kevin off at the mall.
Odd Man Out - S3-E6
Factual error: Near the end of the episode when Kevin and Paul are riding their bikes toward each other before they stop for a brief hello of sorts, Kevin rides past a couple cars parked on the street that were built in the early 1980's. A red Pontiac LeMans and a black Pontiac Grand Prix-both were parked in front of the 1969 Ford Thunderbird.
Factual error: After the failure to get a new car, the family is sitting around disconsolately watching TV, when a commercial for a new Camaro comes on. However, the Camaro shown is a second generation unit, not introduced until February of 1970, and the Arnolds are still stuck in 1969.
Continuity mistake: Back when Ms. White said that she was going to get married over the summer, she should afterwards be called Mrs. Hiemer, as she wrote on the board. But in this episode, we're shown a yearbook, and her name is printed as Mrs. D. Hymer.
Factual error: During the scene when Kevin visits Winnie through the window after her car accident, a song by Bob Seger can be heard playing. While this scene takes place in 1970ish, the Seger song playing wasn't released until 1978.
Continuity mistake: During the party a car horn sounds on the road outside the Arnolds' house - a woman looks out of the window and says "the Fosters are here." The Fosters then appear at the front door in about five seconds after the horn has sounded.
Visible crew/equipment: A boom microphone is visible for several seconds at the top of the screen, as the boys watch a girl walk through the library. The camera pans down to attempt to hide it. (00:01:50)
Factual error: The gym at the "1972" championship game has a 3-point arc. High schools didn't implement a 3 point line until 1987.