In a season 1 episode, Cutter is examining Claudia after she was attacked by the Monster of the Week.
Claudia: "What are you doing?"
Cutter: "I have no idea. I've just seen it on E.R."
The dodo chase in 1x04.
Even better, the massive Mood Whiplash that starts it; the team is all lined up in front of an anomaly that's opening before them, ready for whatever big, horrible monster is about to come out and try to kill them—and then a whole flock of dodos pop out of the anomaly, squawking, running around and looking very, very confused.
One of the dodos tries to run away from someone through a shelf...only to find that its butt is too big for it to fit through!
In the episode with the deadly Anurognathids, a temporarily blinded Claudia grabs a golf club to fight them with. Guess what she says when she hits one:
Claudia: Hole in one!
The reason Claudia is temporarily blinded in the first place is a masterful example of Black Comedy: After the Pteranodon gets tranquilized, Claudia immediately begins chewing out Nick for his recklessness and declares that from now on, she makes the decisions. Cue the half-conscious pterosaur smacking her in the face with its beak.
Claudia in the final episode of season 1, who closes out a conversation with Nick by bringing up a kiss they shared. She tells him that sexual harassment is frowned upon in the civil service and saunters out with a very faint smirk on her face. The shock on his face is priceless.
From the same episode, when the two kiss (right in front of Helen) before Nick enters the Permian. As Helen and Nick walk toward their destination...
Helen: "I take it you enjoyed that." Nick: *grinning like an idiot* "Yep." Helen: "I suppose the object of the exercise was to punish me somehow." Nick: *STILL grinning like an idiot* "Actually it wasn't about you at all."
Nick also gets another funny moment when he says "If I don't come back, push Lester through the worst anomaly you can find," before entering the Permian anomaly.
Season 2, episode 2. A giant worm grabs Jennifer, and Cutter grabs a katana off a decorative mount in the hall to kill it with. Immediately afterward, another worm grabs Nick by the thigh. Jennifer grabs the sword and decapitates the worm, missing Nick's groin by about four inches. Nick responds the way any man would.
Nick:"WATCH!!!! Where...you're swingin' that thing!"
Lester at the end of season 2, when he asks Leek, who is holding Cutter hostage, to hurry up because the snooker is on the other channel.
Lester "being Jess" in Season 4, episode 5 where we basically learn he has no business being in front of a computer.
Any scene that has Lester and Connor in it. Go on, pick any one. It's bound to be hilarious.
Lester: Oh, and if I ever find you socks in the bread maker again, you're fired.
Connor: I was keeping 'em warm...
For that matter, any scene with Connor or Lester works as well.
The very beginning of series 5.
Lester: *on the phone in a traffic jam* Yes I've got an anomaly for you Jess. One of the greatest anomalies known to the western world. Why they call them roadworks...*winds down window and yells at builders who are mostly brewing tea* WHEN THERE'S NEVER ANY WORK GOING ON!
Lester's reaction to finding out the knighthood he was hoping for was always going to Phillip. He repeats "Good, good, good, very good..." over and over as he calmly walks into his office and the door slowly swings shut. We then have a moment of silence, followed by a muffled scream of rage.
Season 5, episode 4. Jess is having an allergic reaction and Becker is trying to make her take some water.
It's Ben Mansfield's expression that sells it, really...
Becker and Jess have another crowning moment of funny when Becker is busy storming a building which they think contains the psycho Ethan and Jess tells him to "Be careful, and keep warm." Again, Ben Mansfield's expression is what makes it perfect.
Also from 5x04, Becker ordered Emily to leave the building with the "other nonessential staff" when there's an incursion in the ARC. Emily, being Emily, ignores him and shows up later.
Becker: What the hell! I gave you a direct order.
Emily: I know. I just thought you were wrong.
It leads to another when Becker basically complains to Matt about it:
Becker: She disobeyed a direct order.
Matt: Yeah? Get used to it.
Again from 5x04, Matt and Connor discuss Connor's plan to collapse an anomaly to kill the beetle swarm with a gamma ray burst and exactly how likely it is that they'll survive...
Matt: So what are we lookin' at here, fifty/fifty?
Matt: Sixty/forty? I could live with those odds.
Connor: Let's just say it's...better than winning the jackpot in the National Lottery.
(on Cutter) Oh, and by the way, Professor Cutter won't like you, and he'll go out of the way to make your job as difficult as possible. Try not to take it personally.
Lester and Becker's dueling Deadpan Snarker personalities is what sells it.
Becker: Well, I have extensive experience in dinosaur hunting, sir. I assumed that was why I was picked for the job.
Lester:(a bit later) And in future, I'll do the jokes.
I've lost count how many times Lester has told Becker off for being snarky, when its clearly Lester's job.
Virtually any and all awkward conversations shared between Connor and Abby in the first few episodes of season 1. Especially when Connor finds out that Steven note who Abby had a crush on at the time has a girlfriend.
In 1.3, when Connor casually asks Steven if he's taken so that he can have Abby to himself. He ends up making it sound like he's hitting on him. Steven's reaction is priceless.
The skirmish with the male raptor in 2.1, particularly the ridiculous motorcycle chase.
When Cutter and Steven get into the elevator to escape from the raptor. Cutter punches it in the face to keep it from getting in with them. Cut to a shot of the elevator going up, with the raptor clinging to the bottom.
3.4, after Danny Quinn lures the Giganotosaurus back through the anomaly in a helicopter, returning without the helicopter.
"Do you want me to go back and get it?"
That bit of Black Comedy at the beginning of 3.5, when the business agent, infected with the fungus, tries to speak to his boss on the phone but only being able to cough and choke. Finally, he vomits up a bunch of spores with the speaker still held against his mouth.
"Alright, you're fired."
In Series 3 Episode 3 when it's revealed that Helen has a clone of Cutter, Lester's only response is: "Two versions of Cutter? It's like some sort of nightmare.
When the gang are at Jenny's wedding in season 4, Conor suggests to Abby that they should get married in the same place. Abby nearly chokes on her wine, thinking he's proposing instead of being hypothetical.
Jenny: Conor, it's customary to propose to the girl before you start planning the wedding.