The guys seemingly violate San Dimas Time at the end of Bogus Journey, but it can be explained if they switched places with themselves from 16 months in the future.
Could also be that Rufus made up San Dimas Time purely to motivate the boys to finish their project on time. Doesn't seem to be applied anywhere outside of their project.
After all, their BODIES run on San Dimas Time, and they were, well, slackers, so Rufus had a good reason to convince them that they couldn't delay, or it would have taken many years to do it. They didn't figure out that they could have dialed one day back as many times as needed.
Of course Future!San Dimas is a utopia - this is a future in which God, heaven and a personification of Death himself are conclusively proven to exist, not to mention time travel (which was probably given to humanity by De Nomolos or Rufus in a Stable Time Loop). This probably goes some way to explaining just how Wyld Stallyns are so massively successful.
Joan of Arc being picked up by Bill & Ted can either be considered Fridge Brilliance or Fridge Horror when looked at from her perspective. There she is, kneeling down in cathedral praying for guidance - then all of a sudden thunder and lightning appear above her head and with a bright light a clear glass confessional appears down in front of her with two strange beings offering their hands to take her to a trip to Utopia. There she sees a world where women are treated equally: there is so much peace that women train in regiments for fun: and she gets up on stage and has hundreds of people listen to her without any form of prejudice. Finally she gets sent back and tells everyone her story of meeting an angel and seeing heaven. It's no wonder they thought she was a heretic.
The first film begins with Rufus explaining how utopian the future is, but he talks about how "bowling averages are way up, mini-golf scores are way down," and Earth has the best waterslides in the galaxy. It seems merely humorous that he would touch on such trivialities, but perhaps this shows that in Rufus's time, peace and prosperity have been known to the people for so long that they don't even care to mention it if someone asked what makes Earth good. Rufus rattles off hobbies and pastimes because life is just so good that it doesn't even need to be mentioned that there is no more war or environmental concern or other things more pressing to modern people.
At the end of the sequel during the end credits montage it is shown that Wyld Stallions music literally makes crops grow faster and better, they devise an air guitar that runs on smog, thus solving pollution, they get rid of nuclear waste by using it to power their amplifiers, their music and message is so strong it brings peace to the middle east. Also during the first movie, they plant the seeds of their philosophy on some future dudes, and even if you are a cynic it is indeed a powerful message and a way to live a better life "Be excellent to each other, and party on!"
Why was the stage set-up and prepared with every prop they needed for their presentation? They engaged in Retroactive Preparation for anything they needed. That's where Gengis Khan got his pole-axe from. They made notes of what they needed and bam! it was there.
In Bill & Ted's Bogus Journey, when the Evil Robot Usses reveal the their robotic innards, it causes many people to faint (even the princesses), yet when the robots do this to the real Bill and Ted, the latter don't seem to faint at all. Immunity, perhaps?
By this point, Bill and Ted are probably quite used to weird stuff happening to them. Of course, the princesses are technically time travelers as well, but still not nearly as used to weirdness as their boyfriends.
Why would everyone go home before the last band played at the Battle of the Bands? The 'Battle' isn't over until every band plays, but apparently in San Dimas, people are content to see a few bands play, and then read about who won in the newspaper the next day.
In "Excellent Adventure", the duo bring a number of famous people from history into the present. Four of these (Socrates, Billy the Kid, Joan of Arc, and Abraham Lincoln) had deaths that could have been prevented if they had known they would happen. By travelling to the future, they have been given the opportunity to learn about their impending deaths and possibly prevent them. Bill and Ted may have altered the course of history.
It's properly a case of Hitler's Time Travel Exemption Act. If they had learned about their personal futures offscreen, there would have been an offscreen conversation that says they have to go through with it anyway to prevent changes to the future.
Even if said historical figures retain their memories of the time travel; all of them learned that they became famous throughout history. Socrates is pretty much the father of philosophy, Billy the Kid got the notoriety that he always craved, Genghis learns he successfully conquers most of Europe and Asia and dies of old age as the Khan, Freud's work becomes the basis of psychology, Napoleon also conquers most of Europe and establishes a successful empire (and he is still regarded as one of the master strategists of all time). The one who gets the rawest deal is Joan, but even then, her 'heresy' eventually results in elevation to sainthood. Since the movie is not cynical at all, apparently they are OK with how their lives turned out.