Revealing mistake: Riggs handcuffs himself to the depressed businessman. They jump off the building but they're not handcuffed to each other anymore. They used plastic cuffs which could separate during the stunt in case anything went wrong. They break just as they jump, so they grab each other's hands to stay in contact. After they land the cuffs are attached again.
Trivia: During the scene in which we see Murtaugh talking to Hunsaker about his involvement with the Drug dealers. Hunsaker mentions 'Air America', a CIA front during the Vietnam. Air America was a film regarding this very thing staring Mel Gibson and filmed three years after Lethal Weapon.