Chapter one.
The BG Chapter is incogruent with the rest of the book. The book encourages you to make a morally grey character with a dark secret because of drama, then expects the same characters to heroically risk going to hell for the good of a totally different country. The first dungeon really demands that your DM softballs you, lest your entire party be TPKed because someone thought it was a swell idea for a bunch of level 2 characters to fight a wizard with access to Fireball. (At 36 average damage, not even a barbarian can tank that.) Along the way the party is introduced to not one but two tag-along NPCs who actually care about Elutrel because the story demands such a thing to actually work, and as established none of the characters are likely to do so beyond the immediate threat of "It could happen here too."
That said, if you ever want to start something in Baldur’s Gate, this book has oodles for that, even custom backgrounds.
Chapter two.
It immediately starts off with an ostensibly good aligned level 18 wizard casting plane shift on your party to get into Avernus, who then immediately casts Time-Stop to get the hell out of hell, leaving your party, and the entire city of innocent people to their fates. High level NPCs not doing anything useful in FR is kind of a dead horse, but come on!
Other than that initial souring, the chapter is one of the better ones in the book. You wind your way across the city looking for survivors, there are a few non-combat encounters with devils, demons, and other evil things to get the party into the mindspace of "Oh, you can actually talk to these things." But also several encounters that are just for violence to remind them that everything in Avernus can and will kill them if so inclined. The chapter ends with most of the NPCs your party has gathered deciding to stay in the city to protect it (I'm looking at you, Wizard, you could have at least done this much) while the players sneak past The Blood War happening under the city to find the McGuffin.
Chapter Three.
Lulu, the amnesiac comic-relief sidekick, leads the party on a while goose chase for a holy sword across the plane, while the party wheels and deals with it's less than scrupulous inhabitants. It's worth noting that you can actually just randomly not end up with the McGuffin at all due to the mechanics of this chapter. The actual plot of this chapter is getting her memories back, and then having someone else tell you where the sword is despite all that hard work you put in.
This is also the start of the "Mad Max" bit of the book. However there is a problem with it, the Vehicles run off of souls. Good characters are going to balk at using them (even if the rule text says it's good to spend a soul coin like this) because it just kind of feels squicky, and evil characters aren't going to risk their necks for this adventure in the first place. There is a splitting path here, but due to the nature of the chapter you are likely to hit up both paths anyway. This is both a good and a bad thing, as the story arc is split up between the two paths, but then again the story arc is split up over two paths so it is also possible to not have half of the story.
In the back of the book there are rules for Infernal Contracts and Devil Charms, which makes this book great if you ever want to do a 5e theme-park tour of Avernus.
Chapter Four.
The PCs find the sword, then enter a memory which is really just a wave-based endurance arena match with some cutscenes thrown in for flavor. Once again, it is actually possible to not get the McGuffin due to the mechanics of this chapter. There isn't actually all that much in this chapter that can be used outside of the adventure itself.
Chapter five.
The entire campaign hinges on a single skill check. If you use the sword and pass you get the good ending. Which is bummer because the bad endings (and there are multiple ways to fail forward in this chapter) are so much more engaging. They include selling your soul to Zariel, unmaking a devilish contract, cutting a deal with a pit fiend or selling one out, allying with Tiamat or one of the Demon Lords, and potentially taking over Avernus for yourself.