Gunnery Sergeant Hartman was either just doing his job and honestly trying to prepare his trainees for war, or his methods were so unnecessarily extreme and brutal that they drove one of his cadets to madness and got both himself and said cadet killed.
On the other side of the coin, some people either see Private Lawrence as The Woobie who was ultimately broken due to being relentlessly bullied by the Drill Sergeant Nasty, while others look at him as someone who really did not have the mental fortitude to make it as a Marine and who really should have dropped out for the good of both himself and everyone else.
Or, it's Joker who is unfit, since he does nothing when he finds Pyle loading a rifle in the head (a violation of at least three regulations). Instead of either taking the (unloaded) rifle away and alerting the MPs, or just alerting the MPs, he just stands and watches Pyle, who has clearly snapped, load a magazine and load his rifle, and as a result two Marines die.
Anvilicious: The 80's saw an unprecedented military buildup and lots of patriotic movies like Top Gun and Iron Eagle which may have well have been recruiting videos. While there were other anti-war films (Platoon being the most famous) this movie definitely made many Gen-Xers think twice about whether a military career was right for them.
Award Snub: It was nominated for one Oscar; best adapted screenplay. It was not nominated for Best Picture, Best Director for Stanley Kubrick or Best Supporting Actor for R. Lee Ermey, despite many people saying they felt that not only did it deserve to be nominated in these categories, but it deserved to win too. Unsurprisingly it lost its one Oscar nod to The Last Emperor.
Hartman's insults are meant to belittle and demean, but one could sympathize with Pvt. Pyle's giggling due to the sheer creativeness of Hartman's ranting. Truth in Television, many Boot Camp instructors are purposefully funny, they try to teach recruits to have the mental control not to laugh, which gives mental fortitude in other areas.
Do Not Do This Cool Thing: Which drove Kubrick absolutely bonkers. Even when he tried to make war as shitty as possible, some people still got off to things like the heli gunner shooting the civilians, and the dehumanizing boot camp led by theDrill Sergeant Nasty. Samuel Fuller called it "another goddamn recruiting film", believing that teenage boys going to Kubrick's picture would come out impressed and seduced by the idea of wartime combat and flouting authority.
Gunnery Sergeant Hartman in general, thanks to the epic performance by R. Lee Ermey.
Pretty much anyone in the US military (and many people outside of it) trying to sound witty and badass will quote selections from the same scene of Hartman singling out recruits in the barracks. Anyone from Texas is probably quite familiar with the list of things that come from Texas.
"What is your major malfunction?" (you know the rest)
"Holy Jesus. What is THAT? WHAT THE FUCK IS THAT?" - Hartman's reaction to finding Pyle's jelly donut. Has since been repurposed to illustrate shock at other things.
"Me so horny, me love you long time" — much to the chagrin of any East Asian woman walking down the street. The controversial Hip-Hop group 2 Live Crew even sampled that line in the song "Me So Horny" on their infamous album As Nasty As They Wanna Be, as did Sir Mix-a-Lot in "Baby Got Back" (albeit only in one line of the song).
Generally speaking, Sgt. Hartman. Tons of people seem to love Hartman, particularly military personnel... when the entire point is that he's meant to be kind of an asshole and, frankly, a somewhat poor drill instructor who doesn't understand Pyle and is ultimately out of his depth in dealing with him. This character deficiency ultimately gets him and Pyle killed, and leaves mental scars on poor Joker. In fact, Ermey, who has been noted for having been a good Drill Instructor in real life, deliberately played Hartman as a very bad one who stays just barely close enough to the rules to avoid being caught.
Almost every YouTube video of Hartman will have some comment along the lines of "My 'Nam drill instructor was just like this, and what he taught saved my life." Whilst not completely implausible, it seems hard to escape the conclusion that a lot of these comments are Phony VeteranYouTube War Experts trying to idolize Hartman and pointing to fictional stories from "the 'Nam" to justify it.
In-universe, Hartman gloats about the Marine-taught shooting prowess of Austin sniper Charles Whitman and Lee Harvey Oswald. Doubly obnoxious because Whitman's massacre would have been barely a year old by the time the movie was set - which, let's again remember, would be the point and the insensitivity is another sign that Hartman isn't a very good person. The problem is, most people don't even remember the Whitman massacre anymore, so it just seems like a trivia piece to modern viewers. On top of this, Oswald actually demonstrates piss-poor marksmanship, with one missed shot, one neck shot and one off-centre headshot when, with a 4x scope at 88 yards, Kennedy's head would have taken up the entire scope.
Moral Event Horizon: The Door Gunner crosses it in seconds as he's introduced killing unarmed civilians, gleefully. He then boasts about his "prowess" and then casually jokes with a technicism when asked how he can kill women and children (and 50 water buffaloes too, all them certified). Ain't war hell?
The Da Nang prostitute ("Me love you long time"), and the door gunner who shoots Vietnamese civilians from a helicopter ("Get some, get some!").
Ngoc Le as the VC sniper. The sniper is slowly built up over the course of several minutes a remorseless and deadly accurate killing machine, picking off the platoon one by one. Finally, they infiltrate the sniper's lair, and the sniper is revealed to be a remorseless and deadly accurate killing machine who's a pigtailed teenage girl. Even after Rafterman empties a clip into her, she still isn't dead, but asks them to shoot her. Joker does so, completing his character arc.
The blanket party scene. Hell, just search up "blanket party" on Google Images right now, and all of the results will almost exclusively be from that scene.
While the Vietnam War half may not be as memorable as the boot camp sequences, there's also the "me so horny" scene, the door gunner scene, the mass grave scene, and the final confrontation with the VC sniper.
Some Anvils Need to Be Dropped: Joining the military is not for everybody, some come out in worse shape than they were going in, often psychologically.
Squick: Pvt. Pyle's suicide. See Nightmare Fuel above for more details.
"Weird Al" Effect: Mention the name, "Gomer Pyle" to someone. A younger person will probably think of "the fat Marine recruit from Full Metal Jacket who blows his brains out" instead of "the gas station worker from The Andy Griffith Show who got a spin off sitcom where he was in the Marines" (Which is where the name came from and why Gunny Hartman gives it to him).
What an Idiot!: Sergeant Hartman notices Private Pyle has a loaded gun in his hands in the bathroom at night, and is aiming at him. You'd Expect: That Gunny would call the guards to take away Pyle. Instead: He continues on insulting Pyle, leading to the death of both of them.