Other mistake: When Robert Downey Jr. lowers the helicopter onto the freeway to yell at the truck driver, he is very close to the truck driver, so close that the truck driver can even hit the helicopter. Why does a long haired man standing underneath a helicopter not have his hair blown around?
Continuity mistake: When Mel Gibson and Robert Downey Jr. are hanging upside down in the copter, the first scene (with the necklace mistake) has Mel in the right seat and Robert in the left seat. When they crash out of the window Mel falls out first from the left seat and then Robert from the right seat.
Factual error: The movie is set in the late 60's. In the restaurant scene two guys on stage are singing "A Horse With No Name" which didn't come out until 1971.
Factual error: The language in Laos is Laotian, but Mel and all the "locals" speak Thai.
Factual error: Billy's helicopter pilot's licence is cancelled by mail. This doesn't happen. First, a pilot has his licence suspended pending a hearing. The hearing takes place, allowing the pilot a chance to defend himself. The tribunal will make its decision and the pilot is advised there and then of the result. It's like a trial, in many ways. This has always been the way, right back to the 1930s.
Factual error: When he picks Billy up with a rope from the helicopter while he is asleep, Mel Gibson flies the OH-58 (Bell Jet Ranger) helicopter single pilot from the left seat. That model, when flown single pilot, is always flown from the right since the only starter button is on the right side collective control, as well as the right side has more instrumentation than the left side.