For a serious novel/musical, there are some funny moments.
The scene where Javert arrests the Thénardiers is one big Funny Moment—i.e., "Would you like my hat?" and "You will not leave by the window. You will leave by the door. It is healthier."
Culminating, when threatened with bludgeoning by Madame Thenardier, with what might be his most hysterical Badass Boast ever: "What a grenadier! Mother, you have the beard of a man, but I have the claws of a woman."
When the National Guard first arrives at the barricade, there's a rather amusing exchange.
Guardsman: "Who is there?"
Enjolras: [singsong] "The French Revolution!"
"I have just met Marius' new hat and coat, with Marius inside."
Half the things Gavroche says or does. The scene where he exchanges insults with a sergeant of the National Guard and then knocks him over with a cart deserves special mention.
Sergeant: "Will you tell me where you are going, you wretch?"
Gavroche: "General, I'm on my way to look for a doctor for my wife who is in labor."
Sergeant: "To arms!"
[Gavroche knocks the sergeant over with the cart]
From the same scene: "Citizen, I have not called you a bourgeois. Why should you insult me?"
Even Hugo's digression on convents has its moments, specifically with the antics of little girls in convent schools.
Combeferre's most effective one-liner in response to Marius' speech on Napoleon: "To be free."
The entire chapter with Theodule trying to get in M. Gillenormand's good graces, and the old man's reply: "You are a fool."
Towards the end of the book, Thénardier tries to blackmail Marius with the knowledge that Cosette is an illegitimate child. Upon meeting Marius, he has to pause and figure out how to best phrase the accusation, knowing that saying "Your wife is a bastard!" will more likely get him punched in the face.
Hugo's aside when Fantine introduces Cosette.
"For Cosette, read Euphrasie. The name of the little one was Euphrasie. But the mother had made Cosette out of it, by that sweet and charming instinct of mothers[...] It is a kind of derivation that confuses and disconcerts the entire science of etymology. We knew a grandmother who succeeded in changing Theodore to Gnon."
The scene where Fauchelevent, after smuggling Valjean out of the convent in a coffin, has to think of a way to get rid of the gravedigger so he can get Valjean out is pretty amusing.
When Marius started to develop a crush on Cosette after weeks of seeing her and Valjean in the park, he found a handkerchief with the initials "U.F" on it which he thought that this belongs to Cosette and that her name must be Ursule (the only female first name with an U). Then, he starts kissing it. When Cosette saw this, she gives him a puzzling look and not to mention, that handkerchief belonged to Valjean who intentionally left it there. That's right! Marius is making out with Valjean's handkerchief!
When Valjean confesses his identity to Marius, Cosette interrupts their conversation. At one point, she jokingly claims that Marius beats her and asks Valjean to defend her. Then she gives Marius "an adorable shrug of the shoulders, and an indescribably exquisite pout," and Marius randomly exclaims, "I love you!," to which Cosette responds, "I adore you!".
Bahorel giving love advice to Joly. Note that this advice involves purchasing a new pair of pants.
"Master of the House". If that ain't Funny Moment material, then there's no such thing as Funny Moments.
Funny taken up to eleven in the 25th anniversary with Matt Lucas and Jenny Galloway.
"Thinks he's quite a lover but there's not much there", and Thénardier has no idea she just said that
In the 10th anniversary concert, since all the actors are seated on stage in between their scenes, they all join in the chorus of this with great enthusiasm. Watching Colm Wilkinson and Philip Quast happily singing along and clapping to the beat, and Michael Ball apparently trying to get Quast to join him in some impromptu choreography, is hilarious.
Depending on how it's played, this exchange:
Javert: Your time is up and your parole's begun. You know what that means-
By the same token, Valjean's description of the circumstances behind his imprisonment. In the production I saw, Valjean and Javert appeared to be partaking in Snark-to-Snark Combat throughout the whole thing.
Thénardiers in general, especially in waltz of treachery
Shared our bread, shared each bone
Treated her like she's one of our own,
Like our OWN, monsieur!"
In the tenth anniversary, the actress who plays little Cosette holds back a smile at this point.
In other productions, young Cosette has an "Are you serious?" look on her face through the entire song.
In some versions of this song, Thenardier mispronounces Cosette's name and his wife corrects him.
Thenardier: Let's not haggle for darlin' Colette...
Mme. Thenardier: Cosette!
Turned into a slight running gag in the 2012 film, where even when the robbery happens, he mispronounces it and Mme. Thenardier corrects him again.
One production this troper saw had Valjean throw the money for Cosette to the floor in front of the Thenardiers, and at first they ignore it and act sad as they say goodbye. But the second Valjean and Cosette are out of sight they go right for the money and are literally fighting each other for it.
The start of Beggars at the feast: "He's not fooled, told you so!".
This troper saw one production where the Thenardiers have a small argument after Marius and Cosette leave. Thenardier wants to leave too ("We've got the money, let's go!") but Mme. Thenardier yells, "No! I wanna DANCE!" There is complete silence for a few moments, while the other guests back away and give them apprehensive looks, before the song starts up and everyone dances.
Here comes a prince / There goes a Jew. / This one's a queer / But what can you do? Especially humorous if Matt Lucas (who is gay) is playing Thénardier.
This part was made even funnier in one production where the man he calls a queer stops short and turns to look at Thenardier with a "The hell'd you say?" expression. The woman he was dancing with seems somewhat less interested in him after that.
"As for you, take this too!" *punches Thénardier.*
"Enough of that! Or I'll forget to be nice."
There's also the part in Plumet Attack where Eponine tries to stop her dad from robbing Valjean's house:
Eponine: I'm gonna scream, I'm gonna warn them here!
Thénardier: One little scream and you'll regret it for a year.
Gavroche after Stars: That inspector thinks he's something but it's me who runs this town!
This exchange from Red and Black
Enjolras: Grantaire put that bottle down!
Grantaire: Give me brandy on my breath and I'll breathe them all to death!
In the 25th anniversary concert, during the robbery attempt, after Valjean and Cosette disappear, Marius is left standing there and realizes they're gone, darting offstage with his hands up and an "I wasn't here!" look on his face.
From the same concert, when Marius is explaining why he's so out of it at the meeting, as soon as he says the word "she", all his friends take on the most knowing expressions. It's entirely nonverbal, entirely background, and entirely hilarious.