Pretty much anything that comes from the Narrator. Helps that he's voiced by Will Stamper.
For one thing there's his poor attempts to keep his story "clean" like with a Last-Second Word Swap on the swear words and other examples.
Narrator: Boy he was pis—he was mad!
Narrator: If I was in your capably nimble shoes, I'd say 'To heck with Hatty and my Friends, they'll be fine!' And then I'd pack myself a nice bagged lunch, show these cats my favorite finger, and make like horse turds and hit the trail. *The puppet gives the cats a thumbs-up*
Narrator: ...I mean you've got these voodoo nightmare princess thingies, easily the biggest crocks of sh—stuff I've ever heard in my entire life, but I'm the dumb one, that's fine.
Narrator: And to ice this little predicament cake of yours, the staff is sick of Hatty's bullshi—b—uh—nonsense.
Then his tendencies to go on long, redundant, and not-quite-appropriate metaphors when it comes to your situation. He's also constantly trailing off, stammering, talking too long and having to interrupt himself, and making revisions to his narration on the fly.
Some of the ways he uses puppets to illustrate his point are also just hilarious.
The demise of Furrham Purrbottom, the founder of the Theater. He loved theater so much that he sat watching his own shows for days on end, refusing to take bathroom breaks, until his body became too full and he shat himselfto death.
The fact that it's not remarked on that during the prologue, as Hatty is saying how upset he'd be if he lost even one of his friends after the first part of the storm has passed... there's already a puppet missing from the boat.