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. (00:47:50)jimba
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.
Revealing mistake: At the end, when all the historical figures are going back into the phone booth, you can see the trap door in the back open and the people go through it. It would be kind of tight to fit all of them in the booth at the same time.