Revealing mistake: When Chewy puts his hand on Han's shoulder at the end, Joonas Suotamo's finger is visible through the fur.

Solo: A Star Wars Story (2018)
1 revealing mistake - chronological order
Directed by: Ron Howard
Starring: Woody Harrelson, Emilia Clarke, Donald Glover, Alden Ehrenreich
Other mistake: Towards the end, Chewbacca and Beckett have walked some distance from the landed yacht. They come up a small slope and are faced with Han, waiting for them. But an aerial shot shows that slope is very short and just runs down to a cliff. There's no way they could have got to the base of the slope to walk up it in the first place.
Han Solo: Since when do you know how to fly? [Chewie howls.] 190 years old? [Chewie howls again.] You look great!

Trivia: In Dryden Vos' meeting room, the golden idol from the opening scene of "Raiders of the Lost Ark" can be seen briefly on one of the tables. So too is Mandalorian body armour, similar to Boba Fett's.
Question: How did Han and Chewie get off the desert planet at the end?
Answer: By the end of the movie, Han and Chewie have been left with some items of worth, plus their smarts and charm. We don't see how exactly but we can assume that's enough to get them into their next adventure.
Answer: I would classify this as the traditional movie serial "cliff hanger" ending where the audience is purposely left pondering what happens to the protagonists and must wait until the next installment to learn the outcome. Considering Solo underperformed at the box office, there is the possibility there may not be another independent Han Solo film. However, the characters would likely reappear in another stand-alone Star Wars film, thus answering how they escaped their situation.
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Answer: Or they could've hitched a ride with the Cloud Riders.