Whopping coincidences and absurdities

Whopping coincidences:
1) Riggs and Murtaugh are taken off the South African drug dealers case and assigned to a completely unrelated task: Protecting Leo Getz... and Getz just HAPPENS to be the accountant for those same South African drug dealers!
2) Vorstedt just happens to be the guy responsible for Riggs' wife's death.

Absurdities:
1) After they are violently attacked and nearly killed, Riggs just casually drops Rika off at her apartment instead of going straight to a police station/military base/bank safe deposit vault/somewhere/ANYWHERE.
2) Riggs and Murtaugh have to be the worst witness protectors in history (or would that be witless protectors?) as they are constantly leaving Leo alone and unprotected.
3) Classic "not in the script" moment: Vorstedt and his men tie Riggs in a straightjacket and throw him in the water. Wouldn't it have been better/quicker/safer just to shoot him?
4) Riggs and Murtaugh wouldn't have just been taken off a case, they would have been prosecuted to the fullest extent of the law for the amount of damage they caused and danger they exposed the public to in the first scene.

I know, I know, it's supposed to be mindless entertainment. And I did enjoy the film immensely when I first saw it nearly 30 years ago. But I have become far more critical and cranky in my old age.