The humorous material in the game can be divided into five categories: things Dalboz says ("You gain 86 experience points and found a healing potion. Oops, um, wrong kind of dungeon master."), Have a Nice Death messages ("At least this is what you assume he does. You are far too dead to know for certain."), moments involving Antharia Jack ("Can I at least have a hug?"), things your three totemized party members say ("Oh c'mon! You gotta be a moron to perform impromptu root canal on a sleeping dragon. It just isn't done."), and everything else ("The Alarm System is down. Can everybody please try and cheer him up?").
The Hades Shuttle Courtesy Phone puzzle is incredibly convoluted, but entirely possible to solve given a time and a notebook. Realizing on a repeat playthrough that Kendall lets you bypass it is hilarious, in an awful way. The spellchecker puzzle is similar.
"A sword on a noose. I like that. It's like soap on a rope, only a little tougher to market."
There's a vent in the Cathedral that the player cannot reach without a rope, but if you don't have it with you you can toss your sword at it instead. Dalboz is dumbfounded.