So Nick, AWOL, dies in Vietnam just as the embassy is falling and the US pulls out.
How then did his body end up back in his hometown? Michael couldn't have dragged it half way across Saigon, got it into the embassy and had it choppered off to a carrier somewhere out at sea.
Or am I missing something obvious here?
Yes, you are missing something obvious. The ability to focus on what's important watching a film - its themes, plot, characters and craftsmanship - and not get distracted by insignificant details. Do you really need to be spoon fed every detail of how Nick's body got back home?
Michael couldn't have dragged it half way across Saigon, got it into the embassy and had it choppered off to a carrier somewhere out at sea.