For those who are interested “The Nitpicker’s Guide for Trekkers” series of books by Phil Farrand covers many of the science problems covered in the above posts.
I would like to make some comments in Star Treks defense, many concepts they use are dead on and were a great improvement form the usual TV Sci-fi.
Trek knows the difference between a galaxy and solar system. How many times did the Galactica enter a “new galaxy”?
Since stars are so far away you need to travel FTL to cover such distances in a reasonable period of time. In order to travel FTL, rocket thrust no matter how much will not do the job, thus “warp drive.”
Great power requirements are needed so they use matter/antimatter annihilation as a power source. You can’t get more bang for the buck.
Two propulsion methods, warp drive for FTL, impulse engines for sub-light speed. The impulse drive is a fusion reactor powered rocket engine with deuterium as the propellant mass. A fusion rocket is not science fiction but a very real possibility. The velocities and accelerations Trek uses however are fiction but even here they are aware that such accelerations would be deadly to the crew, thus inertial dampers.
Trek knows interstellar space is full of dust particles and at high velocities would cause damage to the ship thus navigational deflectors.
At one time or another Trek has dealt with and discussed the following science concepts: antimatter, Quantum mechanics, nuclear fusion, stellar evolution, Heisenberg’s uncertainty principle. When was the last time “The Many Worlds” interpretation of QM was discussed on Friends?
“SF like Star Trek is not only good fun but it also serves a serious purpose, that of expanding the human imagination. We may not yet be able to boldly go where no man (or woman) has gone before, but at least we can do it in the mind. We can explore how the human spirit might respond to future developments in science and we can speculate on what those developments might be.”
Stephen Hawking (from the Foreword: Physics of ST by Lawrence Krauss)