Movie spans in '74-'75, and early they show a joint being rolled on a copy of Hunter S. Thompson's "Fear and Loathing in Las Vegas", with the tagline at the bottom (of the book) "From the author of the Great Shark Hunt", which was published in '79.
In the scene where they are leaving for boarding school, the Bonanza bus has an new Rhode Island license plate (white and blue with the sail/wave on it). When the bus arrives, the license plate is the old "The Ocean State" style.
In the movie, Old Man Dunphy has blue eyes. Later on during a flashback scene, we are shown that Mrs. Dunphy had blue eyes as well. However, their kids - both Jackie and Timothy - have brown eyes. While unusual, there are well documented cases of this.
In Dunph's first day of school, he is in a math class where the teacher calls on him to solve a problem. The problem is written on the blackboard behind him. Later on in the film, what should be months have passed, and back in the classroom, the blackboard remains completely unchanged.