The good bits: there's a decent story, and some interesting political philosophy, which you don't have to agree with. To some extent the book manages to break out of it's own time: the starship pilots are all women, for example.
The bad bits: although the philosophy is interesting, it is one sided, and somewhat wodged in (though not as badly as Rand). And he doesn't manage to break out of his time as much as he'd like.
Reading stuff like this - and, for that matter, the film, which is also very of it's time, just a different time - I'm reminded of a scene from Asimov, nominally set tens of thousands of years in the future, when a man corrects a woman's (Bayta's, I think) estimate of her weight by sight of her upper arm. In this one it is perhaps the scene where he is reconciled with his father, who explains that his mother just couldn't understand. It's all so 50s America. This is reflected in the grunt's view of women; by the strict segregation on the ships; indeed by the school scenes. However, his political theory has it that only veterans can be full citizens, so it is necessary for women to be able to serve, and so he allocates them a place as pilots. Given that his MI (Mobile Infantry) all wear power armour this makes no sense. I don't think it would have disturbed his story (in the film it doesn't) but perhaps it would have, to readers of his times?
Of the political philosophy, it is of a limited franchise, a topic perpetually recurred to by folks who dislike the excesses of democracy (among which I count myself; I've not I think suggested limiting franchise, which I think doomed, but more limiting governmental power). Ironically, this was in the 50s, a time that people now look back on as a semi-golden-age of quality politics and political debate. Never believe the myths of a golden age. We are "taught" this by our narrator siting in class: at school via flashback and in officer training. Disappointingly, though, when it comes to the explanation of why vets-only should be selected his ultimate justification is "it works"2. Since this is in an imaginary society, this is unconvincing. He also offers "because people have demonstrated putting themselves between society and harm", which kinda works in a war situation but not in the peace situation where as he admits most recruits were given make-work. And then we're left I think with his "because it demonstrates that people have put group good ahead of individual good". This is better and rather more convincing; though undercut by the obvious: anyone power-hungry will hardly cavail at doing two years of service1. In peace time, that would be a low bar; possibly he is arguing that even that low bar, by reducing the franchise to perhaps 10% of the population, would be effective? Perhaps, though not obviously so.
But we have to turn to the glorification-of-the-military component. It would be interesting, in a way, to have the same book about their society written 50 years earlier, with no enemies to fight, and see how things were justified; but we don't get that. Instead we get what I think reads very much like something written about USAnian servicemen in WWII would read like. Pretty well everyone in service is good, and he gets away with this because he has winnowed out the bad. The MI get to kill gooks because bugs-are-bad (or in another way, can be killed because not really sentient, being controlled by a "brain" caste). They are fiercely loyal to their own. So it is very hard to take his "limited franchise" not to mean "military only" franchise, and outside his strongly idealised view of said military, it's hard to see that making sense.
One of the scenes that I very much objected to when I first read it as a ?14? year old, was the discussion of "life, liberty, and the pursuit of happiness". Now I'm much more sympathetic to RAH's views; though I'm disappointed he doesn't put forward the view that govt is instituted to protect rights, not give them.
On a trivia note, he calls HMS Shannon HMF Shannon, which is careless.
In the end, I think the book though flawed is significantly better than most of the stuff from those days; perhaps I should try to read Glory Road again (update: I did. It was disappointing). By failing to extricate militarism from service it ostensibly fails in its fundamental purpose. That same failure has kept it read. Do most, regrettably, pay more attention to the militarism than the service? I suppose that I don't know.
Notes
1. The closest this gets to mention is the scene where one of his fellow trainees fails to "freeze" and is drummed out for hitting a superior; our hero overhears a sergeant and officer overhearing what a shame this is, as the chap had political ambitions.
2. Collections: How to Roman Republic 101, Part II: Romans, Assemble! tells me that middle-republic Rome worked somewhat like this: voting in the law making assemblies was weighted towards those who had served in the army.