Deliberate mistake: When Basil is arguing with Polly and eventually decides to call O'Reilly, he trips over the gnome. However when we see Basil come out from behind the desk, he takes the gnome out of a side gap in the desk, perfectly out of reach of Basil tripping over it. (00:14:30)
Deliberate mistake: After Barney buys the car from Mrs. Lesh, he and Andy are standing at the steps as he tells her not to look back at the car, and the next shot of Andy and Barney at the front door is the same shot from a few moments prior, but it's been flipped so they would be looking in the opposite direction. (00:09:30)
Deliberate mistake: In the opening scene, Wood's tie is grabbed by an exposed fan belt located above the side of the engine. However, this belt/pulley assembly doesn't exist in a real truck's engine compartment - the fan belts are all in front of the engine, where the camera can't see them easily. The prop master must have added this dangerous device to the truck to allow the camera to see the strangulation.
Deliberate mistake: In season 4 episode 7, 'Brian the Bachelor'. Cleveland is sitting in a chair in a waiting room and is getting really nervous. Peter tries to help him by tying him to a chair and when that doesn't work, he takes off all of their clothes. Peter ties Cleveland's hands to the arms of the chair and then takes Cleveland's clothes off. He couldn't have taken the shirt off while Cleveland's hands were tied to something without untying him or ripping the shirt, which he didn't do.
Deliberate mistake: In this episode Lucy is trying to get Ricky to notice that their anniversary is on Monday the 19th by showing him a large calendar with the 19th circled. However, when they are in California and they celebrate their anniversary and Ricky asks for information to be wired to him, the telegram tells him that their anniversary is on the seventh.
Deliberate mistake: Lindsay is not at Caleb's funeral in the last episode of season 2, "The Dearly Beloved". It's unlikely that she would have missed it - she is still on good terms with him and he is her father, the only reason she left was to be with her mother, not because she didn't love Caleb.Obviously they didn't want to create another drama with having Lindsay there while they had to focus on the important story-lines - Caleb's death, Kirsten's drinking and Marissa shooting Trey.
Deliberate mistake: In the first few series, it is suggested Lister and Kochanski barely know each other. In 'Balance of Power' Holly says that Lister has only ever spoken 173 words to her. However, by series 4 Kochanski is referred to as Lister's ex-girlfriend with whom he shared a relationship. In the series 4 documentary, Doug Naylor explains that Lister's attitude towards Kochanski was immature in the first series which is why they changed his back story from wanting to be with Kochanski to actually having been with her by series 4.
Deliberate mistake: Hank only discovers the tattoo on the back of his head after having his hair shaved off. There is no way, however, he wouldn't have noticed it before this. The tattoo artist had to shave hair off the back of his head before putting on the tattoo. While he might have not realised right away, the pain the following day and the fact that he would have noticed a large part of his hair missing would make it unavoidable.
Deliberate mistake: When Elaine comes home and doesn't find Sean Paul there, she runs to her neighbour across The Apartment. The neighbour opens the door and stands outside it then the door slowly closes behind him. Suddenly, the door opens again with a swoosh without anyone being there. Because the camera switches angle right after this, it is apparent it was opened to gain this shot or to at least permit it continuity wise. (00:16:40 - 00:17:10)