Anyone who expects to see much science in anime science-fiction is bound to be disappointed. Anime sci-fi has much more in common with fantasy than science. Most of the shows I've watched focus on the social, economic, political or personal effects of technologies, not the technologies themselves. Take Dennou Coil for instance. How exactly does Yasako pick up Densuke when he's just an image she sees with her special glasses? How about the "parallel universes" in Noein? Sure the story does make references to the "many-worlds" interpretation of quantum theory and even includes a cameo appearance by Schroedinger's cat, but it's all just handwaving in order to build a structure on which to tell a much more personal story about Haruka and her friends. I haven't seen many shows from the 80's and 90's to know whether they have a larger component of "hard" science-fiction, but shows from 2000 onwards rarely have that focus. Planetes is probably the closest example I can think of.
I find it better to consider shows like these and Shin Sekai Yori as "speculative fiction" rather than "science fiction."