Without mentioning the basic story line, because it is covered by other reviews, I'll just hit on a few random points that struck me.
There are perhaps two dozen characters in the book, scattered all over the world (the "multiple viewpoint" approach). Many of them in the course of their conversations mention the names of real-world science-fiction authors (Heinlein, Wells, Clarke, Burroughs, etc.) as if those sci-fi authors are universally regarded as authoritative celebrities and are guiding philosophers for humanity. Why did Leiber do that? Was he intentionally sucking up to his peers? Trying to elevate his field? That was a poor device to include in a work of fiction. The effect is to remind the reader, "Don't forget, you are reading a science-fiction novel right now."
When the feline alien gave her big speech about the need to rebel from authority in order to live life to its fullest, it was as if Leiber were reaffirming (sucking up) to the youth of the 60's and telling them they are correct in their rebellious urges. But at the same time, he depicted the human teenagers in the book as wild, drunken savages bent on destruction and menacing society. Mixed message? There is also a parallel between the second visiting planet (described as the "police") and the human police on Earth who are engaged in battle with the rioting teens.
I didn't like the extreme coincidence that the one person the cat-alien snagged from the Earth's surface was also the friend and colleague of the astronaut who was pulled from the moon, and both happened to be romantic interests of the female protagonist who was carrying the vital spacegun to the Earth authorities. I hate it when authors get lazy with coincidences like that.
Leiber's depiction of the "weed brothers" was extremely shallow and comical. First time I've heard a character say "Daddy-O." He certainly treated the pot-smokers in disparaging terms, but later in the book when Cat Alien was giving her big speech, he seemed to glamorize (suck up to) the drug culture of the day when he had her explain, "We want to range through *mind* more thoroughly -- that crumpled rainbow plane inside our skulls."
"Bad Future Prediction" Department: "Not for the first time Richard reflected that this age's vaunted 'communications industry' had chiefly provided people and nations with the means of frightening to death and simultaneously boring to extinction themselves and each other." Heh heh. Nice try, Fritz. That sounded like the guy who predicted the telephone would never be useful.
The book could have certainly used another chapter, an Epilogue, to discuss the Earth's healing efforts afterward and the newly acquired wisdom that was gained after the crisis had passed. An "epic" of this size should have included that. As it was, the book just stopped as soon as the visiting planets vamoosed.
All in all, a fine disaster sci-fi story, with a great premise (cookie monster gobbles up our moon), adequate commentary on human reactions to it, and wide-ranging action.
4 stars if compared to only science fiction; 3 stars if considered as just fiction.