Both the opening of the third movie, and the little bit after the ending credits. Especially the latter, where Riggs and Murtagh show up just before the bomb goes off - and they take off like a bat outta hell.
"My mom says cops shoot black people!" Riggs busted up laughing, and it looked to me like Mel Gibson was genuinely laughing, too.
The look on Roger's face when he realizes the commercial Rianne was in is a condom commercial.
Followed by that guy who was building Roger's hobby room commenting about how she was so good in the commercial, it made him want to go out and buy rubbers. Riggs barely contains his laughter.
Much later, Leo is watching TV and sees the commercial and Roger quickly tries to cover up the TV.
When that smug prima donna director fires Rianne on the spot, Riggs convinces him to hire her back at a higher salary by smacking him around like a redheaded stepchild, while passing it all off as an attempt to help the director back to his feet.
And then, once he smacks some sense to Murtaugh... well, see Papa Wolf.
Riggs ramming his dislocated shoulder into a wall to re-set it with a massive grimace of pain—six inches in front of his psychologist's face. She just gives him a resigned look.
"How do I know you're the police?"
"After I shoot you through the door, you can examine the bullet! Open up!"
After Riggs and Murtagh are demoted, they have to deal with a jaywalker. Said jaywalker turns out to be a little obnoxious, so Riggs deals with the problem by pretending that they're just gonna kill him.
In 4, Riggs keeps hanging the picture of Murtaugh in his underwear. Murtaugh is getting more than furious.
Murtaugh:This shit ain't funny anymore!
After the two were promoted to captain, they see it again.
Riggs: Could we please knock out this shit already? This is your captain speaking.
He then puts it back up immediately after Murtaugh walks away.
Also in 4, Butters arrests a Chinese person who's at the wrong place at the wrong time.
Butters: You have the right to remain silent. SO SHUT THE FUCK UP. You have the right to an attorney. If you cannot afford an attorney, we will get you the dumbest fuckin' laywer on Earth. If you get Johnnie Cochran, I'll kill you!
[Riggs is about to drive up onto the center divider of an overpass in Trish's new car during a pursuit]
Murtaugh: You're not going to make it!
Riggs: Yes, I will.
Murtaugh: [anxiously] There's not enough room!
Riggs: There's plenty of room, sure I'll make it!
[Riggs runs the car up onto the divider, scraping it along a metal guard-rail]
Murtaugh: [screaming as sparks fly] Ah, my side panel!
Riggs: Goddamn it, you were right. There wasn't enough room.
The "rubber" tree that the other officers leave on Murtagh's desk after his daughter's big break... in a commercial for condoms.
Lorna takes Riggs back to her place after a mission. While Riggs jokingly fiddles around with Lorna's stuff after she told him not to, he happens to find a The Three Stooges video game on her computer, much to Riggs' amazement since he too is a fan.
Even one for the bad guys as in the climax of part 1, when Joshua heads for Murtagh's home in revenge for foiling his scheme. Thankfully no one's home but he gets spooked by the TV playing A Christmas Carol
Scrooge (On TV): You boy? What day is it today? Joshua: (Shoots up the TV) IT'S CHRISTMAS! (Keeps firing)