The "Unfinished Business" is pretty dark, but it has a hilarious moment. Jayne tells Niska that the Alliance has a bounty on River, in order to make sure she isn't hurt. It turns out her bounty was cancelled, but there is a reaction nonetheless.
The next ten minutes were the bureaucratic equivalent of open-mouthed, slack-jawed horror at the realization that River Tam was in the hands of Adelei Niska.
The third story arc "Mosaic" is filled with these, generally mixed in with Crowning Moments Of Awesome. Among them are Mal expying Captain Hammer and Jayne pulling a Dan McNinja by setting himself on fire and chasing down the enemy pirate crew's Knife Nut. There's also Mal's reaction to River getting drunk and having a lesbian moment with another girl, and River's constant berating of Mal for not getting her any chocolate.
The air was also filled with curse words. They didn't make a whole lot of sense, or maybe the people the Captain was yelling at were supposed to be open-minded by enjoying fornication with both livestock and amphibians.
Or maybe Mal was just so angry he was getting shot at over a box of puppies that he stopped caring about his curses being comprehensible.
The entire "voice-recording" scene in the "Charity" arc.
River channeling Jayne and naming her sword Laertes.
Kaylee and Wash's increasing boredom sitting on Serenity in this arc, not knowing that the other crew members are in the middle of a gunfight with a team of mercenaries.
Inara's distraction of the authorities in "Condor."
The epic expansion of the geese juggling gag in "Silver."
Wash's assessment of the Hands of Blue.
"So, they're like zombies," Wash said, nodding. "Power armored government zombies. Shiny."
River caltalogues her injuries after a particularly brutal fight against some pirates, ending with her sunburn.
Pretty much all of River's mental snark during the Fourth Interlude.
Nearly any scene involving River and Jayne, when it isn't a heartwarmer. Like the scene in "Silver" where River annoys Jayne into letting her climb up onto his back so she can see what the rest of the crew are oogling, or the "You. Me. Shower." line in "Charity."
Jayne giving Inara romance advice. Valid romance advice. In most fics it's the exact opposite.
In Wrath, the "training montage" sequence where River repeatedly gets her ass kicked by Doctor Rashid, who, in her own words, has a third of his body mass devoted to his beard.