Actually, I don't think the plausibility of the science or other gadgets actually has much to do with the division between science fiction and fantasy. It has much more to do with feel and tone. I offered Card's comment that "science fiction has rivets" tongue in cheek, but I think it gets at the real distinction -- much more so than trying to classify stories based on the plausibility of their scientific premises.
As wakela pointed out, Star Wars is science fiction because it has robots and spaceships, not because the "jump to hyperspace" is scientifically plausible or the way the TIE fighters move has anything to do with the way real objects behave in a vacuum. Ditto Star Trek. What makes it science fiction is that it has gadgets that look and behave like extended versions of stuff we see around us (whose physical operating principles we typically don't understand anyway) and the characters talk to each other using a vocabulary that sounds like an extension of our scientific-rational worldview. It's that tone and feel that defines the genre (and more importantly, attracts a specific audience) rather than finding a physicist to sign off on your particular flavor of FTL drive.
Similarly, Lord of the Rings is fantasy, not because the Dark Lord or the elvish "straight path" is scientifically implausible (give me a few minutes, and I could concoct an explanation for either one that sounds as "scientific" as anything used to justify a phaser) but because they're explained in mythic and magical terms, and the characters talk to one another in a language that sounds like an extension of an older, more "spiritual" world view. Neverwhere does the same thing in a modern setting. "London Below" is spirit-infested, and filled with magical beings, in the way we all once believed the whole world was populated with spirits. Again, it's the tone, feel and vocabulary that defines the genre, not the plausibility or implausibility of the props.
At least, that's my take...