This movie in particular doesn’t mention Vietnam (unless I missed it).
But if a movie is set in the '70s it usually feels obligated to include something about Vietnam (along with other '70s trappings: disco, bell bottoms, Nixon, porn). I actually can’t think of an example right now.
Actually, whippersnapper, Vietnam didn’t become a pervasive presence in film until the 80s. Obviously, it was there, explicit or not, in some 70s films, but it wasn’t until the 80s that the nation seemed ready to start processing or exploring it, whether via serious dramas like Platoon or cartoonish action films like Lethal Weapon. (And those are just two examples that deal with it explicitly and in the visible text of the film.)
Anyways, if a detective movie is set in the '40s or '50s it’s assumed the men in the movie fought in WWII.
But if a similar movie is made in the '70s there’s no obligation to mention that, for instance, young Gosling was drafted and sent to Vietnam in 1965 after the Gulf of Tonkin incident.