How does Riggs unwind after his first day with a new partner? He finds an underage prostitute and gives her $200 to watch The Three Stooges with him. Her delighted reaction just sells it.
Riggs' Christmas present for Roger at the end of the first film - the bullet he was going to use to kill himself
Lethal Weapon 2
Riggs courting Rika, Dutch girl working for the South African consulate, was adorable as the two obviously liked each other.
Riggs and Murtaugh bonding with Leo, whom they initially find repulsive. Its subtle, but its because of their budding friendship that the officers go above and beyond the call of duty to protect Leo. As a result, they make a lifelong friend...wholl never shut up.
When a distraught Riggs calls Murtaugh and tells him that the South Africans killed Rika and declares war. Murtaugh immediately stuffs his badge in his drawer to go help him.
Lethal Weapon 3
The simple fact that Leo is still around, having maintained his friendship with Riggs and Murtaugh, years after his case with them has ended.
Riggs befriending an Angry Guard Dog and placating him with the dog biscuits he was using to kick his nicotine addiction. The best part? He adopts the dog and still has him in 4.
Riggs' dog Sam appears in all four films. Shetland Sheepdogs have a lifespan of 12-14 years, there's an 11 year gap between the first and last films, and he was already fully grown in the original. Riggs is great with dogs.
Riggs sounds very pissed after Leo has been shot by Travis. Even though he annoys them and they mess with him, Riggs does care about Leo.
Lorna deciding to let Riggs in on her investigation.
Roger trying to teach his son how to shave after accidentally killing one his best friends. The film could have played up blaming him for the shooting: nooope, he blames his friend for getting involved in guns. So do the dead boy's family, who rather than be angry at Roger are angry at the gang their son was in.
Doesn't stop Daryl's mother from slapping Roger.
At the climax of 3, Travis is bearing down on Riggs in a construction vehicle. Murtaugh has a machine pistol loaded with cop killer bullets, a massive grudge with Travis, and a clear shot, but Riggs is in his line of fire. What does he do? Toss the gun to Riggs so that he can finish Travis off without taking any injuries.
The very end of 3, which is a Bookend to the start of the original film. Murtaugh's family surprise him with a cake to celebrate his retirement whilst he's having a bath, but he tells them that he wants to stay on the force for a bit longer. They completely support his decision, even after all the times he's almost died since the original film.
Then he pulls Trish into the tub after their children have left. Awwww.
Lethal Weapon 4
The first is when Riggs is trapped under a chunk of concrete underwater, and Murtaugh is searching for him desperately. Murtaugh yells out for Riggs to will him towards his location, and he somehow knows to dive underwater to save him. For bonus points, this is the one time they agree to go on the count of 3 with no discussion.
The second is Riggs' final visit to his wife's grave, saying that although he's ready to move on with his wife, he'll always have their wedding ring. Riggs is looking for a sign that Vickie is okay with it, and gets it, oddly in the form of Leo.
Leo's poignant story about his pet frog Froggie. Also a bit of a Tear Jerker. He explains that he didn't have any friends growing up except Froggie, and he accidentally killed him. Leo eventually made friends with people, and they weren't better friends than Froggie, just different, thus in his own way telling Riggs that it's perfectly okay for him to find love again.
A subtle moment: Riggs tries to apologize for him and Roger always picking on Leo. Leo's response is "it's ok, it's ok", but not said in his usual frenetic annoying matter, but very calmly and reflecting a greater amount of maturity.
Equally subtle, so much so it might even be a Throw It In!, but as they're getting Leo into the photo, Riggs refers to him as "my best man."
When Lorna goes into labor, Leo rushes Riggs over to the hospital. As the soon-to-be new parents get rushed into the delivery room, Leo is left outside in the hallway with a "Yeah, okay....I'll wait here" dejected manner....only to have Riggs run back out of the room and glomp him.
The Finale Credits not only show photos of the characters and moments, but also the cast and crew from behind-the-scenes. All while "Why Can't We Be Friends?" and "Pilgrim" play in the background. The last photo is a large one with everyone. And the series literally comes to a close as the photo album closes.
Riggs and Murtaugh's on-screen chemistry was so real, the actors couldn't help but become real life friends as a consequence.