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: 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.
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.
Continuity mistake: The items on Chuck's lunch tray - particularly the milk carton - keep moving around between shots as he's speaking to the pretty girl.
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.
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.