The same scene, as Annie explains why they called Sam in:
Annie: We were hoping you could be a voice of reason... Sam Tyler:[Feverishly intense] I came out of a musical box. Annie:... a stabilizing influence...
Chris's date in the third episode of second season. First Ray suggests he gets her drunk, so Chris got drunk and...threw up all over her. It loses something in description but it's hilarious on screen.
"... WE ARE THE LAW, you bloody clowns! God help us!"
In the same episode: MrsLuckhurst. Especially if you follow a certain line of thought on what, exactly, her party trick was...
"You are surrounded by armed bastards!"
The opening scene from 1.02, wherein Sam, Gene, and Chris are chasing a suspect while wearing speedos. Even more hilarious are Chris's Swimmies and Sam getting whacked by the old woman with the bag.
Sam reading suspects their rights and being told, "That's not how it goes!" Also the time he reassures a scared witness being asked to pick somebody out of a lineup that they won't be able to touch him or even see him, because he'll be behind special glass. Gilligan Cut to the witness just standing in the canteen within arm's reach of a row of Death Glaring thugs. Afterwards, Gene turns to Sam and says, "'Special glass'?", and somehow it sounds like the stupidest thing in the world even to an audience that's used to two-way mirrors.
"I met a bird. Medical bird." "Yeah, they're called nurses."
Gene Hunt's Pocket Protectors in 01-06. "What are the chances of that?" "Pretty good actually."
The scene in 2.4 where Chris has a bit of an accident in a cramped "surveillance" van.
Gene: What have you been eating, Pedigree Chum?!
In the second episode, Sam, Gene, and a witness are staking out a neighborhood in an ice cream truck so the witness can identify a suspect without being seen. There's just something blackly hilarious about a bunch of little girls skipping up to the truck to buy ice cream, the Gene Genie giving them the British equivalent of the finger, while eating an ice cream cone himself, and the girls running off crying.
In 1.3, Sam tries to explain to Gene that the street they're parked on is one-way. Gene reverses and smashes through a pile of boxes, while holding a roll in his mouth, to Ballroom Blitz.