When Brie Marschz (Catherine Keener) and Dana Marschz (Steve Coogan) are arguing in the Mexican restaurant in the middle of their argument, the margarita glass disappears when the camera cuts to Catherine and returns when the camera cuts back to Dana.
When the drama students are forbidden to stage their play on school property, they move the show to a warehouse used for raves because promoters won't be using it because they are at Burning Man Festival in Nevada. But the play supposedly takes place near end of traditional school year (May or June) and Burning Man always takes place on Labor Day, in September.
In Hamlet 2, the play within the movie, Hamlet forgives his father, but Hamlet has nothing for which to forgive his father in Shakespeare's play. If there's anyone Hamlet could forgive it's his father's murderers, Hamlet's mother and uncle. However, even though this could be a mistake on the Dana Marschz's part, he does prove himself knowledgeable of Hamlet, otherwise he wouldn't have been able to write a sequel.
After Mr. Marschz trips on acid, the police find him naked from the waist down on an abandoned couch. When he is picked up and escorted to a car, his shirt parts briefly and we can see that he is wearing flesh colored underwear.