Dystopia Is Hard: It's repeatedly stated that the slugs, despite their utopian claims, make horrible masters they over-exert their hosts, starve them, and are ignorant of basic hygiene.

And the entire novel takes place during the shirtsleeve months of a single year. The slugs invaded Russia just three months before the US, and just before the climax, Asia is depopulated by a revival of the Black Death. The slugs themselves are literally filthy, as they never make their hosts bathe.

Dirty Communists: A Heinlein favorite and in this case, an Incredibly Lame Pun.

Department of Redundancy Department: After Mary's 'clueless chick' act fails to work on the men at the fake saucer site, she states that they can't be 'normal male men'.

After marrying Sam halfway through the book, she becomes an instant 'Yes dear' housewife, though it's unclear whether this is Values Dissonance on Heinlein's part or if he's just playing the situation for its humorous aspects.

Chickification: Mary is a secret agent who carries an excessive amount of firepower and is certainly willing to use it.

Calling the Old Man Out: Sam's father is actually nicknamed 'the Old Man', which may be an allusion to the Old Man of the Mountain.

Bizarre Alien Reproduction: Each 'slug' can consume the bodily resources of their hosts to fission into two daughter parasites at will.

Benevolent Alien Invasion: The aliens claim to be bringing inner peace to humanity.

Beastly Bloodsports: The Puppeteer Parasite aliens decide they quite like this aspect of human culture, and decide to liven things up by giving the bull an even chance by having one of them take over the bull so it's as smart as the matador.

Then there's humanity's first response to the alien invasion being to institute mandatory nudity.

Author Appeal: Sam is a cat lover and has a thing for redheads, much like Heinlein himself.

Not much, eh? Most minds stall dead when faced with facts which conflict with basic beliefs “I-just-can’t-believe-it” is all one word to highbrows and dimwits alike.

The Old Man’s unique gift was the ability to reason logically with unfamiliar, hard-to-believe facts as easily as with the commonplace.

The puppet masters robert heinlein