Alternate Character Interpretation / Designated Hero: Stock exchange fraud, rigged voting, hypocritical "anarchists" who deride "government knows best" philosophy right up until they form a shadow cabinet that "knows better" than the government they helped construct; not to mention the strategic use of weapons of mass destruction to terrorize the Earth's population into caving to their demands after they asphyxiated the previous "head of state" into a vegetable state... Our heroes, ladies and gentlemen!
Seinfeld Is Unfunny: As noted on the main page, the book pretty much invented things like Colony Dropping and virtual acting, but nowadays those things are so commonplace in science fiction that the book's presentation of these concepts is unlikely to even raise an eyebrow, much less come across as brilliantly fresh.
Technology Marches On: Played straight and averted. Mike's processing power, when drawing on the entire computer network of Luna, is portrayed as almost inconceivably fast. Mannie is amazed that Mike can create and animate a lifelike computer graphics representation of himself, saying that such a feat would require millions of calculations per second — in supercomputing terminology, multiple megaflops (FLoating-point OPerations per Second). The first supercomputer capable of more than one megaflop was the CDC 7600, which was completed in 1968, two years after the novel's publication. That machine took up a large room; half a century later, hardware of equivalent power is so small you could swallow it without noticing it on the way down, and so insignificant that nobody would notice the loss. But we still have yet to achieve the sort of genuinely photorealistic, indistinguishable-from-human realtime animation Heinlein describes — we can do realtime animation, and we can do damn-near photorealistic animation, but not both at once, and we still can't quite do truly photorealistic animation at all. (Avatar might still be as close as we've come thus far, and the whole film took somewhere around a millennium of processor time to render.)
Part of the problem of reaching photorealistic animation is that our visual medium keeps getting better. Photorealistic might have been easier to achieve if television quality stopped improving in the 60's. Grainy, low-res, limited color would be much easier to fake on the fly than million-pixel resolution HD content. It's just another aspect of Zeerust, where a technological revolution wasn't foreseen (in this case the advancement of TV past tubes).
Values Dissonance: Even allowing for the deliberate differences in Luna society, the book was obviously written in The '60s in light of its characterization of women.