Rereading, though, I find the editorial one-liners that introduce each story rather lame and occasionally irritating. (Karen Anderson's delightful 'Landscape with Sphinxes', one of the stories I remembered exceptionally well, is introduced simply 'And then there were none' - which doesn't seem to have much at all to do with the content.)
This anthology was published in 1978, but some of the stories date back to the 1950s, and before: real Golden Age stuff, with all that that implies: occasionally bland or clunky prose; extravagant and now discredited predictions for the future; reliance on a punning punchline; and a healthy dose of sexism. (Even when they aren't human, females are mysterious and unpredictable, and over-emotional, and flirtatious ...)
Asimov's introduction clearly stuck when I first read it:
In the short story, there can be no subplots; there is no time for philosophy; what description and character delineation there is must be accomplished with concision ...in the short short story, everything is eliminated but the point. The short short story reduces itself ot the point alone and presents that to you like a bare needle fired from a blowgun; a needle that can tickle or sting and leave its effect buried within you for a long time.
There are stories I wouldn't bother reading twice, because they rely (like a joke) on a punchline, and when you know it the story's purpose is complete. There are others that are masterful capsules of what-if; Stephen Goldin's 'Stubborn', in which a stubborn fellow gets what he deserves, for instance, or Frederik Pohl's 'The Deadly Mission of Phineas Snodgrass', an alt-history classic. And there are stories that are gems, so tightly packed that there might be a whole novel in there -- the aforementioned Karen Anderson story, for instance. (This is one reason I write short fiction from time to time -- to get the idea out and into some shape, rather than expanding and filling up my head.)
A good antidote to the current trend for long and wordy novels ...