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.
Mel Gibson references the Three Stooges several times in the film. In real life, Gibson is a big Stooges fan, and in 2000, he produced the biographical TV movie "The Three Stooges."