Continuity mistake: The location of the comet in the sky changes direction at several points. Whilst it's apparent size and altitude will of course change, the direction it is coming from cannot. As an example, it is seen looming over the power plant towers, but when Ned is on the hill, it's no longer there.
Audio problem: After Homer puts the old milk in the fridge and Bart takes a drink from it you will then see Marge use a fork to take the milk out of the carton. Marge says "woof" but her mouth does not move in sequence with the audio.
Factual error: In "Nightmare On Evergreen Terrace", Martin has a dream, in which he speaks Latin. At one point, he says a verb that doesn't exist: "morire". The words is "mori" (to die), "moritur" (noun dies) or "moreris" (you die). The "moirie" is also on the blackboard behind Martin.