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.
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.
Add timeJeff Swanson
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.