When this show premiered Spielberg was at the top of his game/fame. He was a director(Jaws, Raiders, ET) and executive producer(Gremlins, Back to the Future). Amazing Stories was a big event series. It had a million dollar per episode budget(quite high for the 80s), state of the art title credits and many famous faces(especially behind the camera). It didn't even need to show its worth in the first season, it was locked in for two seasons. Alas it was mostly a dud, and was nowhere near as good storywise as the original Twilight Zone or Outer Limits.
There was no equivalent of "To Serve Man" or "Nightmare at 20 000 Feet" in Amazing Stories. No "Zanti Misfits" or "Architects of Fear." Stories that you could watch once and probably remember well, and be able to relay to someone else in a few sentences and still be entertaining because the idea was good.
The best live action episode was in my opinion, "Mummy, Daddy." It had energy, humor and clever ending, which was improvised, and if it had followed the script as originally written(concluding in the hospital) would have been a dud as well.
"Family Dog" also stood out.
I remember "the Main Attraction," "The Mission" (mainly for the cartoony ending), "Gather Ye Acorns," "Miscalculations," "Mirror, Mirror" and "Go to the Head of the Class."
But beyond some fancy special effects and occasional laugh, the stories just don't hold up.
Doing a memorable anthology show is hard, but the cheaper Tales From the Darkside was locked into the horror genre and didn't do so badly.
The most memorable thing about it was in fact the opening credits, and as others have said, the series never lived up to the concept. It was probably held to a higher standard because of Spielberg's film history at the time, but for the small screen, he was no Rod Serling.