The chalkboard gag is a reference to the fact that the Treehouse of Horror episodes usually air sometime in early November.
The robot Bart and Martin invented is actually a real product http://www.parorobots.com/. Based on the academic papers publication date from the website, it can be concluded that the Simpsons episode was inspired by this research project.
Bart previously won an SES science fair in Duffless and Treehouse of Horror VII. Unlike these episodes, he didn't steal anything from Lisa's science project.
Agnes mentioned that she carried Seymour around in her womb, but Skinner is Armin Tamzarian, not Agnes' son. Maybe she was dismissing the real Skinner. However, it may not be considered a goof as the episode Boy Meets Curl reconnected Seymour's origin again back to his pre-1997 origin.
In the scene where Homer shows Roz the coffee room, his tie is pink, and not green and blue like in the previous scene. His tie also switches colors from pink to green and blue throughout the first half of the episode.
Homer was demoted for bunking off work, but that isn't grounds for demotion, it is grounds for dismissal.