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. Also the onscreen graphic says it's 1810. (00:47:50)
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.
Character mistake: In the movie they grab Genghis Khan in 1209 which would have been correct, he ruled Mongolia from 1206 to 1227. In the presentation at the end they say in 1269 he did this and that, that would have been Kublai Khan's reighn of terror in Mongolia.
Other mistake: Beethoven didn't seem fussed nor resentful of Napoleon being part of the group. Historically he temporarily admired him and wrote the Third Symphony inspired by Napoleon's ideals of Europe's new hope of enlightenment but later despised him after he crowned himself Emperor of France in 1804 and furiously scribbled out his name off the title page of his Third Symphony and named it Eroica which he originally titled it as "Bonaparte Symphony" due to his former admiration of Napoleon.
Plot hole: It seems that after committing 6-odd counts of aiding and abetting, literally right in front of the strict Police Captain father of one of them, Ted and for that matter Bill, would be lucky to only go to military school, regardless of passing or failing one particular class.