Factual errors: There is a heinous number of most egregious factual errors in the depiction of the famous historical dudes, their lives, their works, their time periods and the state of their hearing.
Continuity: When the phone booth is first created we see it start to form, then we see a shot of Rufus' face with a complete booth reflected, then back to a shot of a still-forming booth.
Continuity: When the phone booth first appears to Bill and Ted at the Circle K, we can see it dropping straight down, but in the next shot, when it lands, it drops at an angle.
Revealing mistakes: When Socrates pushes a British knight off the horse-drawn wagon during the escape to the phone booth, it's quite obviously a stunt double, most notably by the man's face.
Continuity: When Rufus leaves in the phone booth (at Ted's house) and the empty booth drops down, Bill and Ted are right next to each other in close shots, but are 3 or 4 feet apart in the medium/long shots.
Continuity: People endlessly swap places in the ever-expanding phone booth. Sometimes they disappear altogether.
Continuity: In the beginning when Bill and Ted are leaving class, the writing on the blackboard clearly says "Ghenghis Khan". A few seconds later it says "Genghis Khan"
Continuity: A podium appears and disappears between shots at the end of the movie.
Continuity: In the saloon fight when Billy the Kid is caught cheating at cards, a prostitute swings in on a rope and takes a guy through a window with her. The rope she swings on disappears and re-appears a few times between shots.
Revealing mistakes: When the historical dudes are filing into the phone booth at the end of the movie, you can see a trapdoor in the back open as they go through it.
Revealing mistakes: When the phone booth is first created we see a reflection of the phone booth in Rufus' glasses with the word "Phone" across the top, but in a reflection the phone booth and the word "Phone" should be reversed.
Continuity: As Bill and Ted are about to journey off from Ted's house for the first time, his dad's police car jumps between the driveway and sidewalk several times.
Revealing mistakes: When the phone booth lands at the Circle K for the first time, you can see when the booth lands that the antenna on top of the phone booth falls off and then re-appears in the next scene.
Boom mic visible: In the steady cam shot inside the jail, as the camera leads to Freud, just as the angle is about to change the boom mic drops in and out of the screen.
Continuity: At the end of the film, onstage during the presentation, the phone booth antenna is undamaged and shows no traces of the "gum and cans" repair done earlier in the film.
Errors made by characters (possibly deliberate errors by the filmmakers): When Bill & Ted pick up Genghis Khan in Outer Mongolia, it's the year 1209 as indicated on the screen. However, during the final report, Bill says they picked him up in the year 1269.
Continuity: The sequence with two sets of Bill and Teds is much longer the second time around. Most noticeably, the first time as shown doesn't allow time for the "later" Bill and Ted's conversation with Rufus to take place.
Anachronisms: When Bill and Ted go to the old west, they go into a saloon and order a couple beers. When they turn around and lean back against the bar, you can see their beer bottles have flip-top lids, which didn't exist in the 1800s.
Errors in geography: When Bill and Ted arrive in New Mexico, the phone booth lands in front of a Saguaro cactus, which does not grow naturally in New Mexico.
Errors made by characters (possibly deliberate errors by the filmmakers): When Bill and Ted land in the future and they tell Billy and Socrates to stay put, Socrates nods in understanding. However, in Greece nodding means no and shaking one's head means yes.