Two instances: Both are presented in a comedic manner and technically avoidable.
The first one is avoidable since it involves slapping Ronny the locksmith outside of Megg's Buttery goods multiple times, doing so however only involves him spewing a little onscreen complete with a sound effect. This is not required to progress the story.
The second one is during the final part of the game and is also avoidable as long as you don't touch the analogue stick during the part where the two children (Billy and Turpentine) ask you to spin them around. Yes it can elongate that section but at least you'll get some more funny dialogue out of it, and it will continue after only a few repeats.
They will not vomit however once they ask you to "Send us flying down the road!" Spinning them will launch them both in separate directions instead of making them both barf with a comedic "BLEUGH!".
It is implied that Herbert wets himself after you get the hose working for him in his garden, since his pants are wet, yet the hose in his pocket comes out dry.
Several characters say "Reggies wife could learn a thing or two" after the player does some strange handlings like gripping the mower or slapping a fish (pretty sure its played for jokes, but i put it here just in case!)
During the ending segment, Sam the butcher get's his hand stuck in the meat grinder, it is up to you to grind up his arm or not.
"Me arm is in the bloomin' thing!"
SPOILER: There is a possible/secret scene after entering the Inn where larry starts listing things and becoming more incomprehensible, and theres a popup with
"think F.A.S.T.
F ace - is it too big for their head?
A re they having a stroke?
S
T ime to call the coastguard"
im not sure when it shows, but its after having entered the Inn several times. It starts when Larry lists his favorite ales