Anachronisms: In the background in the orchestra scene, a Sabian cymbal can be seen. This scene takes place in 1966, but Sabian Cymbals was founded in 1981.
Errors made by characters (possibly deliberate errors by the filmmakers): In the Dewey Cox Universe, "The Dewey Cox Show" airs on CBS. During a rehearsal, Dewey complains that his show is getting beaten in the ratings by "The Incredible Hulk." "The Incredible Hulk" aired on CBS, so it could not be in competition with "The Dewey Cox Show."
Anachronisms: During his show at the college for "little man", contemporary cars can be seen in the background.
Revealing mistakes: The sink Dewey pulls out of the wall in the recording studio shatters when it hits the floor, which did not happen to the other sinks he pulled out, and would not have happened in real life.
Anachronisms: In the scene where young Dewey and his brother are talking about what they'll do when they grow up, Nate mentions being "an astronaut." The scene is set in the early 1950s; the word "astronaut" had not yet been coined.
Anachronisms: In the flashback to Dewey's childhood in 1946 Alabama, his brother expresses his future wish to become an astronaut and go to the moon. This probably would not have been his career option since the first man didn't go into space until 1961.
Anachronisms: During the black and white concert sequence from the sixties, the cars in the background are modern.
Continuity: When his wife is leaving him, she leaves two kids on the couch, which Dewey just looked at saying he didn't need them.
Boom mic visible: In the scene right after Dewey and Darlene get married, before Edith walks in, a boom microphone can be seen in the upper right corner.
Anachronisms: When Darlene is talking to Dewey about quitting the LSD in the studio, Sabian drum cymbals are clearly seen in the background. This scene was supposed to take place in the 1960s; the company was not founded until 1980.
Revealing mistakes: When Dewey's first wife is holding two babies telling him that he doesn't spend enough time with his kids, you can clearly see that one of the babies is a doll.