It's a journalist's telling of a fictional war story set against the Vietnam War background. There's been a lot of attempts to interpret the film, but the truth of the matter is that it's just the story of one young man's fictional journey through boot camp and into the war itself.
The film looks at some of the scenes of everyday life in the Vietnam War, but doesn't take a side on the war itself. You hear some of the reasons for the war told from the soldiers' perspectives, and their emotions on the war and reasons for it, but the film doesn't present a pro or con view of the conflict.
So in a sense there is no point to this film other than to show a story of it. What you take away and interpret is all from the audience, and not the film maker.

The main point is to lock up your stuff, and particularly, don't bring jelly donuts into the barracks, especially if your a fatbody.

I agree with much of what has been posted, but I would like to add that I think at least one of the points of this movie is the dehumanizing of men necessary to become "killing machines". That was the point of the basic training sequence being such a long part of the movie. At the beginning the characters are "boys" but by the end of basic training they are "killing machines". Watch what happens every time the group is shown marching, they slowly evolve from uncoordinated "individuals" to a coordinated unit one unit, not individuals. They lose their individuality, and as the beating scene of Private "Pyle" shows their humanity.
Unfortunately, this is still a timely message and a problem. If men have to become this dehumanized to win a war, something I don't doubt, then what do you do with them once they return to "civilization'?

That's what makes the movie so good. It's a movie about nothing. It was like Seinfeld, it was a show basically about nothing. If someone asked me what the movie was about, I would tell them it's 2 hours of beep awesomeness.
Don't get hurt kid. I'm not your daddy, I'll beat you senseless.

The point of the movie is the duality of man.

"War is bad". "Prison is bad". "Crime doesn't pay". "Drugs are bad." "You can't keep a good mad down." So, you don't have to bother watching anything.
Irony is like goldy or bronzy, but it's made of iron.

Dude, the girl herself asks/ begs them to kill her. On the BluRay commentary it is explained/ confirmed it was an act of merci from his side.
It's okay, but you didn't understand the movie.

To the OP, Joker said it himself "the Jungian thing, Sir" the duality of man. Vicious and cold blooded one minute, compassionate, sensitive the next. The killing of the girl at the end intended to show that contrast and did so very well. Joker killed her out of compassion as opposed to vicious revenge although Animal Mother said he was 'hardcore' for doing it Joker didn't want to leave her to be eaten by the 'mother loving rats'.
Well this statement reveals that you have no compassion. Further if Kubrick intent in this scene was to portray Joker as compassionate, it fails.
Everyone in the scene was standing around saying that nothing could be done for her. Wow! how great. He blew her brains out. What nonsense. Let's see what might have been done.

1. Call for a medevac (like they would have done for any American) none of those Marines were doctors so their prognosis is in doubt from the beginning
2. Stop the bleeding
3. Treat for shock
4. Inject her with a morphine syrette from a dead Marine
5. See if anyone had a clandestine pint of liquor
6. See if she wanted a drink of water
7. See if she wanted a cigarette
8. Put her head in your lap
9. Hold her hand
10. Speak to her in a calm soothing voice
    It never ceases to amaze me how many people are so blithely willing to ascribe the most heinous deeds, (also illegal in this case), to compassion.
    But just to end on a friendly note, I hope you are never the victim of anyone's compassion.
    'Ave a nice day.
    I've lived upon the edge of chance for 20 years or more
    Del Rio's Song

That American tree needs blood. Young blood. Blood from home, blood from across the sea.
Buy The Ticket, Take The Ride

To the OP, Joker said it himself "the Jungian thing, Sir" the duality of man. Vicious and cold blooded one minute, compassionate, sensitive the next. The killing of the girl at the end intended to show that contrast and did so very well. Joker killed her out of compassion as opposed to vicious revenge although Animal Mother said he was 'hardcore' for doing it Joker didn't want to leave her to be eaten by the 'mother loving rats'.
Life is always intense for a repo man.

The point is being born again hard. Joker accomplishes that in the end.
"facts are stupid things" Ronald Reagan

What's the point of war? It ruins people's lives and minds. And for what? Why would we fight and kill fellow human beings? This is an anti-war film. That's the point.

The way I see it, the movie has no point or real purpose because Kubrick wanted to show how the Vietnam War and the motives behind it were pointless and not justified

The point is that we are in a world of beep

Sometimes a movie is just a movie.

Yes. And that whole sniper sequence was the Vietman War in microcosmthe hi-tech rich American forces entering into a war fought by people who used any means necessary to fightusing women, civilians. It's like Cowboy said'that sniper's just tryin' to suck us in one-at-a-time.' But American leadership was dragging us into the 'big Muddy' of an Asian war. The majority of the Vietnamese peoplethe North Vietnamese and the Viet Cong in the South, saw Americans as foreign occupiers, just like the French and Japanese before them, which was understandable.

Nice summary.
And now we see similar situations in Iraq and Afghanistan. With all our military might and budget being the only world superpower, these invasions should be a layup, but war is profitable for everyone involved and the desperation to keep the world currency flowing. Now in the absence of a superpower, we have to fight an ideological/tactical boogeyman "Terrorism".

The point was that Vietnam was pointless.
The people of South Vietnam weren't willing to fight for or support the oligarchy that ruled their country. American troops were fighting a limited war for untenable political objectives we would have had to have kept fighting and pouring troops and lives into in order to maintain the status quo. Yet the American governments had been blatantly telling the American people for years that victory was just around the corner, when clearly that wasn't true.
Men fought and died for pieces of land that the minute they left, control reverted back to the enemy in many cases. So they literally died for nothing. In many cases it was impossible to tell who was our enemy and who were our allies among the Vietnamese people. We weren't just fighting soldiers but women and children as well, which was an unpopular situation domestically and with American troops. We obtained no traditional objects of war, capturing and holding territory, defeating and breaking an enemy government,
Thirty years after when this film ended, 1968, we were trading partners with the People's Republic of Vietnam. They are firmly part of the world capitalist economy. So what did all their fighting for a Communist state achieve? Where they in fact committed Communists or was allying with the Soviets are cynical calculated choice to avoid being dominated by the Chinese or foreign colonialist powers?
I think Kubrick did a excellent job of portraying this situation.

Films don't always have to have a point, sometimes they just tell a story. It's a story of a guy (Joker) going through basic training, then being deployed during the Vietnam War. I honestly think that they probably intended to spend more time in Vietnam and less in basic, but they just couldn't cut anything R Lee Ermey did. To me it always seemed that the second part had more of a story to tell, but they just ran out of time. This movie could have easily been at least 3 hours long.

So what am I missing?
Obviously you are not missing anything. Seems you enjoy the film. If someone asked you "what's the point in toilet paper?" I'm sure you could muster a response.
He killed sixteen Czechoslovakians. Guy was an interior decorator.

we already know that ''war is bad'', so there's no need for Kubrick to tell us.
I'd say that not all of us know that. This isn't a cautionary tale or morality play. It's a screen adaptation of a semi-autobiographical novel called "The Short Timers" by Gustav Hasford. Perhaps the question of what it's about would best be posed to Hasford but, like Kubrick, he's dead. So there goes that.
Since the third act is basically a mish-mosh of material from the novel, some of Joker's journey from Parris Island Marine recruit to Vietnam squad leader gets lost in the translation from novel to screenplay (which is weird because Hasford and Kubrick co-penned it).
-Rod