There is an astonishingly funny scene around the mid-end of the second season where Gordon Cole (played by David Lynch) tries to flirt with Shelly Johnson. The running-joke of Cole's hearing problems is made fresh and funny, and adding the Log Lady into the mix just made it even more amazing.
And adding onto that, Bobby's expression when he walks in and sees Cole and Shelly kissing is something that must be seen to be believed.
And of course, Cole's comment on the situation is perhaps one of the best lines in the series:
"YOU ARE WITNESSING A FRONT THREE-QUARTER VIEW OF TWO ADULTS SHARING A TENDER MOMENT."
In one scene in the second season, Windom Earle is listening to the police discussing his schemes via a Tracking Device in their office when Cole suddenly notices the bonsai tree where the device is hidden and leans over it:
Cole: REMEMBER THOSE OLD WORLD WAR II MOVIES? BONSAI!!! Earle:(clapping a hand to his ear) Agh! Damnation!
The scenes where Ben Horne looks back on his childhood.
The drunk Icelandic delegation on Cooper's inn floor. And Cooper's Tranquil Fury at it.
Cooper: Dianne, it is 4:28 AM. I have just been woken up by the most God-awful racket, which you can probably hear over the sound of my voice. (holds up tape recorder for two seconds.) Can you hear that? Up until this moment, I've experienced nothing at the Great Northern Hotel but the most pleasant, courteous service imaginable. However, it just goes to prove the point that once a traveler leaves his home he loses almost 100% of his ability to control his environment. Dianne, I was wondering if you could overnight express to me two-pair of those Ear Pillow silicon earplugs which I used on my last trip to New York. Naturally, I didn't bring them with me on this trip because I didn't feel it would be necessary, however...(holds up tape recorder for three seconds, then turns it off)
Pretty much any of the guests in the background at the hotel. They range from cheerleaders, to marching bands, to a barbershop quartet, and many more. They're never explained, never even really acknowledged, they're just...there. It just seems too bizarre to have a fairly quiet scene of Dale and Albert talking over coffee, when there's a barbershop quartet humming to themselves in he background!
Cooper and the llama.
Ben's mental breakdown and re-enactment of the Civil War in the second season.
Notably her first time waking up, where she breaks the chains holding her down on a hospital bed so that she can start clapping enthusiastically in preparation for a cheerleading routine. The look on Ed's face is hilarious!
Later in season 2, when the pageant judges are discussing what they want in a Miss Twin Peaks, a very exasperated extra walks in front of them carrying a stuffed deer. It looks like he's having sex with it!
The scene where Garland Briggs slaps a cigarette out of Bobby's mouth, causing it to land in Mrs. Briggs's meatloaf.
Cooper's deductive technique involving the throwing of rocks at a glass bottle.
Audrey's successful attempt to wreck her father's impending deal with the Norwegians, by informing them of Laura Palmer's murder.
Speaking of Audrey: The cute moment when she flirts with Cooper for the first time, and Cooper pointedly asks her age. She tells him she's eighteen. Beat. Cooper sets a dinner date.
Hawk: One woman can make you fly like an eagle, another can give you the strength of a lion, but only one in the cycle of life can fill your heart with wonder and the wisdom that you have known a singular joy. *Beat* I wrote that for my girlfriend.
"I've got good news. That gum you like is going to come back in style."
The sound effects on the hospital food. And the actual look of it.
Pretty much anything that comes out of Andy's mouth. "I'm a whole damn town!"
Cooper seeing the array of doughnuts in the pilot:
There's something darkly hilarious about the Waiter's senile antics as Cooper is lying on the floor, suffering from two bullets to the stomach. By the middle of the conversation, Cooper gives up on getting any help and just indulges the man with his trademark thumbs up.
The reveal in season two that after days of investigation, multiple trips to the Black Lodge, what seems to be months of general nonsense, and Cooper getting shot and recovering, that Cooper has only been in Twin Peaks for twelve days.
Albert, at Gordon's behest, coming to check up on Cooper during the Windom Earle case.
Lucy's reaction to seeing Sheriff Frank Truman suddenly walking into the station, not realizing that while talking with him he had walked back from fishing and was talking to her on his cell phone. Upon seeing him, she screams and falls backwards in her chair.
Also this interaction between Cole and Albert.
Albert: Agent Preston gets carsick. Cole: Albert, we're in South Dakota. Cossacks are in Russia Albert:CARSICK!
If you're an X-Phile, just the sight of a David Duchovny character in a high-ranking position in the FBI can be humourous.
The entire sequence of Mr. Jackpots. All of it.
In a very dark way BOB failing spectacularly to imitate Coopers mannerisms and eccentricities, instead coming off as an unsettling Faux Affably Evil version. Neither Albert nor Gordon buy it for a second.
Part 5 is no slouch in amusing moments
The scene with Sheriff Truman and his wife, where she rants him nearly nonstop about a leaking pipe while Truman, clearly used to her behavior, just waits for her to finish up with a "You're impossible!" before she stomps off and he resumes his work.
Cooper taking Frank's coffee because he so badly want it, which ends up with Frank drinking an extra green tea lattee and finding himself really enjoying it.
Doctor Jacoby has become an Alex Jones expy and he sells Golden Shit-Digging Shovels for 29.99 plus shipping and handling.
Albert parks his car in pouring rain, laboriously makes his way outside and locks the door while unfolding an umbrella, and yells "FUCK GENE KELLY, YOU MOTHERFUCKER!"
Richard's response to being shown up by Red's magic trick intimidation.
And let's not forget Ike, a strange little dude murdering people with an Awl and suddenly acting distraught when the murder weapon breaks after a particularly gruesome hit job.
Janey-E's rant against the Loan Sharks is mostly just awesome, but also hilarious from how utterly impudent it is for her to be doing this. Made even better by the loan sharks' faces during and especially after the rant, which can be summed up as, "...What the hell just happened?!"
Coop and Janey-E are attacked by Ike, and Coop promptly takes him down. This would normally be considered an awesome moment, but what pushes this into funny territory are the unrealistic karate chop sound effects used whenever Cooper throat-punches the hitman and the sudden appearance of the Man from Another Place, commanding Cooper to "SQUEEZE [Ike's] HAND OFF" in a voice that sounds like someone had just inhaled a can full of pure helium.
Diane's Catchphrase is, "Fuck you, [name]." When Tammy says something, Diane politely asks her name, and then says, "Fuck you, Tammy."
While Part 8 is full blown Mind ScrewNightmare Fuel that'd give Inland Empire a run for it's money, one part is funny. While their performance is equally nightmare fuel incarnate, just the fact that the Roadhouse introduced them as TheNine Inch Nails can get a chuckle for some. Especially for NIN fans who tend to facepalm at people thinking it's a band when it's the highest example of I Am the Bandnote Granted NIN can be considered a duo now due to it being Trent Reznor and Atticus Ross now but still.
In what should be a Tear Jerker, Hastings' meltdown during his interrogation takes a rather absurd turn when he starts sobbing and telling Agent Preston, "I want to go scuba diving!" Of course, since this is a David Lynch series, it may have been intentional.
Mackley: I'm sorry, Ma'm, you can't smoke in here. Diane: ...It's a FUCKING MORGUE! *puff*
Gordon Cole and others go investigate a location related to what happened to Bill Hastings. As Gordon approaches the specific spot, he sees a dark vortex forming in the sky and spends a good while staring at it. While what is shown from Gordon's perspective is eery as all hell, the funny part is when in the middle of the scene we are shown how it looks to everyone else: Nothing is happening, and Gordon is just standing there, looking upwards with his hands raised for no apparent reason for a good minute and a half.
Hutch and Chantal's first stop after killing Warden Dwight Murphy? Wendy's.
After building up a half of season, we finally get to see what happened to Audrey Horne. As it turns out, she's unhappily married to a man named Charlie and is cheating on him with another man named Billy, who may or may not have connections to a woman named Tina. An Anti-Climax and trolling at its finest.
The shear litany of swears and insults Audrey throws at her husband could give Diane a run for her money.
Cole inadvertently yelling at everyone he's the phone with, causing them to move some distance from it.
Freddie uses his "strength-enhancing" glove to save James from Renee's jealous husband by hospitalizing the latter with a solid punch to the face, prompting several viewers to begin cracking One-Punch Man jokes.
After watching Richard Horne explode through a pair of binoculars, Jerry has a freak-out. In context it's pretty unsettling and heartbreaking, but out of context watching a crazy old man yelling "BAAAD BINOCULARS! BAAAAD BINOCULARS!" and smashing his binoculars to pieces is very Narmy.