I had one hilarious moment with Cassandra. It was on one of her cutscenes, where you catch her reading Varric's book. She slams the book shut and says something like: 'It is trash literature and I have better things to do!' She walked to the left, and the game crashed. Her embarrassment took the entire game down.
Second moment that made me laugh quite a bit was the elf Inquisitor telling a story during wicked grace about her clan. At the end of the story, Cole just smiles and goes: "I liked the part about the rabbit!" I don't know why it got me, but the way it was said just made me laugh.
Then there's a few 'hilarious in hindsight' moments where someone gets a little too close to figuring Solas out and he gets flustered. After the ball, Solas actually disapproves when you press him on what he said during the party while tipsy. He reads one of Varric's books and asks Varric if he thinks that everyone around him is hiding something or a spy. Or his barely contained annoyance when he argues with Morrigan about Fen'Harel.