The Lethal Weapon series, starring Mel Gibson and Danny Glover, has cult status worldwide and is one of the best buddy-action-movies of all times. The first part was even nominated for an Oscar in 1988 ("Best Sound").
Today, it's common practice to release multiple versions of one movie, but back then only a few "Director's Cuts" were released.
Along with the Alien series, especially the Lethal Weapon series is known by the fans for subsequently releasing longer versions. In part 1, there were over 7 minutes of new material added, which mainly show Riggs's self-destructive and desperate ways more explicitly, but also feature Roger's problems with aging.
All in all, the 5 scenes round the movie a little...but you can watch both versions without worries. Especially, since the "COMPLETE EDITION" released in 2007 features both versions.
Uncut Original Version = 105:05 minutes
Director's Cut = 112:17 minutes
The Director's Cut contains 3 new scenes (or 5 single scenes) and thus runs 432 seconds (7,12 min) longer than the original version.
The runtimes in this article of course refer to the Director's Cut.
08:42-13:49 (Attention, splitted into 3 scenes for clarity)
Scene #1: Riggs gets dressed - you see many scars on his back - and loads his gun. He eats a bite (but spits it out immediately) and takes a sip of beer. In the background, some commercial yacks away, Riggs freaks out and throws the bottle at the TV. He calms down, walks to the destroyed TV, puts his wedding photograph back up and promises to buy a new one.
Scene #2: Roger at the shooting range. He streches his hand out, it's shaking. He concentrates and tries a second time: no shaking. Happily, he starts shooting. After he looks at his hits, he wishes himself a happy 50th birthday.
Scene #3: Riggs sits in his car and hears of a shooting by radio. When he arrives there, he learns that there is a sniper shooting at defensless children and that he already wounded a policeman. Since it's not clear, when the special unit will arrive and the guy isn't a very good shot, Riggs decides to confront him directly. Determined, he walks towards him without any cover. They shoot at each other, but miss. Only after Riggs provokes him again and the sniper leaves his cover, Riggs shoots him. Riggs throws away his cigarette and leaves the premises just as the SWAT team arrives (much too late).
[307 sec. altogether]
It's evening and Riggs "surprises" his dog with the new TV he bought.
Riggs pays a young prostitute $100 in order to watch the "Three Stooges" with him.