Stupidity: It was pure stupidity for Riggs to bring Rika back at her residence after escaping the hit on Riggs. The villains know where Riggs' love interest lives and this nor the option to hide somewhere else or safer never occurs to him?
Stupidity: When the guy is escaping on the helicopter at the beginning, the cops are all in position pointing their guns. Despite the baddie shooting at them, not one cop bothers to fire back (despite being fully within their right to). They just stand there and let him escape.
Answer: This scene is already in the movie (maybe only the Director's Cut). Riggs surfaces just off the pier, picks up a chain, strangles one man with it and breaks the other man's neck. The scene is cut considerably for play on television and in all versions of the movie in the UK prior to the 2010 UK blu-ray release (including the Directors Cut) - although some TV airings since 2000 have used the full uncut version.