While later Rambo films lean more and more heavily into the pure action-flick style, the original Rambo film, First Blood, shows a man who clearly has severe PTSD, and a very tough time coping with it. The police mistreatment exacerbates this and drive him to desperation, in part based on flashbacks of his treatment as a POW that the station causes him. Likewise later in the film this discussion with his former commander reduces him to not mere tears, but a bawling mess as he recounts how tough a time he has had since the war.
Did this have much of an impact in the discourse at that time surrounding PTSD and the trouble some Vietnam veterans were having reintegrating into civilian society?
Broadly speaking, PTSD was a fairly known thing by 1982; 'rap groups' (associations of Vietnam veterans) in the US were pushing for the disorder to be recognised as a 'real' mental disorder from very early on (in practice, meaning that it would be recognised by insurance companies, leading to a greater ease of getting compensated for psychological therapy sessions, etc). By 1975 it was actively being investigated by a taskforce of the American Psychiatric Association, which in 1978 decided that it would become part of the next edition of the Diagnostic and Statistical Manual - the DSM-III released in 1980. The psychiatrists were not really on the forefront of the movement to make it real; they were responding to community pressure from groups like the rap groups.
As such, while it was first officially a disorder in 1980, obvious depictions of Vietnam veterans with PTSD go back well before 1980. A paper by Arno Görgen specifies the films Taxi Driver (1976), The Deer Hunter (1978) and Apocalypse Now (1979) as being the mainstream films that most clearly and prominently represented responses to on-going trauma being experienced Vietnam veterans. Travis Bickle in Taxi Driver, according to a paper by Patrick Hackeling:
elicits the entire spectrum of PTSD symptoms. He has difficulty falling and staying asleep, is irritable and prone to outbursts of anger, finds it difficult to concentrate, maintains an exaggerated startle response, remains hypervigilant at all times, has lost interest in activities and life in general, feels detached from others and emotionally numb, and senses the limitedness of his future
Rambo: First Blood, in terms of filmic depictions of PTSD, transforms the 'crazed loner' stereotype behind the likes of Travis Bickle into a trope that is more 'misunderstood hero', which Görgen and Hackeling see as an indicative of an attempt to reintegrate the Vietnam veteran into society during the more patriotic/militarised Reagan years. Insofar as it influenced the discourse, it was as a somewhat more sympathetic re-evaluation of what was a tricky position to be in. Görgen also points out that the Rambo films played upon the widely believed but widely debunked myths of American soldiers being spat upon and booed at returning soldier parades, probably giving that trope a wider audience, and subsequently making larger amounts of American veterans believe that they had experienced something similar in the years after they returned from the war (but which can be seen as heavily symbolic of the dilemma of the Vietnam veteran who experienced traumatic circumstances but did not receive social standing for doing so, and did not receive much consideration from society, broadly, for a long time) - /u/bernardito has discussed this myth in a few different threads, such as this one.
It was broadly in the late 1980s and early 1990s, says Görgen, with films like Forrest Gump or Born On The 4th Of July where the filmic depictions of Vietnam veterans moved away from 'crazed loner' or 'misunderstood hero' to a more nuanced take on the war, where soldiers are shown grappling with how to reintegrate into society.