The red and white Ohio license plate on Toby's station wagon was actually in use during the years of 1976-1979. Since he was going to see Revenge of the Nerds (1984), the correct Ohio license plate would have been blue lettering on a white background which was issued during 1980-1984.
Joyce Brabner comes by train from Delaware to Cleveland to meet Harvey Pekar in 1984. However, the Genesis engine shown pulling the train did not enter Amtrak's fleet until 1993, and the Amtrak logo on the engine is the post-Acela version (2000).
In the establishing Manhattan skyline shot before one of the David Letterman sequences, what was then (the 1980s) the Pan Am building is shown with its current "Met Life" signs (which didn't replace the "Pan Am" signs until 1992) shining from the top.
When Joyce Brabner is running through her personality disorder diagnoses, before she says her "delusions of grandeur" line, we see the phone and an open Fruit Cup near it. The scene is set in the 1980s, and the plastic fruit cups weren't on store shelves until the late-'90s or early 2000s.
In Joyce Brabner's comic book shop in Delaware, she is looking for the new issue of American Splendor, issue #8. American Splendor #8 was published in 1983. There are several promotional posters on the wall of the comics character Concrete (the black, white, and yellow ones that say "Can't find what you're looking for? Just Ask!"). The first Concrete story was not first published until 1986. (The poster wasn't released until much later.)
The exterior front of the comic book store shows a wooden structure with windows that reach about half way up the height of the building and a wooden door with a glass section in it. The interior view shows glass extending from the ceiling to the floor and no wooden door.
The circumstances of the Pekars adopting Danielle were fabricated for the film. Among other things, Frank Stack (the artist who helped Joyce put together "Our Cancer Year") is not Danielle's biological father.