Although I'm not a massive Star Trek fan, this recent Letter of Note about the TV series is quite interesting.
Two months after Star Trek premiered, the acclaimed science fiction writer Isaac Asimov (author of I, Robot amongst other things) wrote an article in TV Guide entitled: 'What Are A Few Galaxies Among Friends?', complaining about the lack of scientific accuracy in Star Trek and its contemporaries. Gene Roddenberry, the show's creator, was a huge fan of Asimov's work, and wrote him a strong-worded but polite letter explaining the lengths they went to ensure scientific accuracy on the show.
You can find both sets of correspondence here. Seems logical enough.