Other mistake: At the Circle K when future Bill and Ted have finished talking to present Bill and Ted and go back into the phone booth, where are the other 5 historical figures? Especially as it is emphasized that they are all squished together, when they land you can see Beethoven, but he isn't there at the end when they leave.
Continuity mistake: In the beginning, when Bill and Ted are at the Circle K and the phone booth lands with their future selves in it, you hear Bill say "Aw, I hate that part" just as they land in the booth. At the end when we see them land to talk to their past selves, Bill doesn't say that.
Factual error: When Bill and Ted grab Beethoven, we are shown the piano he was playing which is a Steinweg (Steinweg later changed his name to Steinway when he immigrated to the United States). Steinweg made their first piano in 1835, and the model shown was built in Braunschweig so must have been made after 1858, but Beethoven died in 1827, years before a Steinweg piano existed.