Consider this is the same year that Star Trek began on NBC-TV. We may laugh at the funny SFX on TOS, but compared to this film (and several others made about the same time), it was downright modern.
Also, consider four years later, Kubrick would make 2001: A Space Odyssey, which to this stay still looks fairly fresh. Check out the 1960s-era reel-to-reel tape recorder the "Educator" uses to record her lessons for the children. At least the Star Trek folks tried to simulate a technology 200 years in the future.
The story-line is about par for the "sturm-und-drang" type of space opera of this time, but it is rather unrealistic to expect us to believe that this crew would be so misfit and unable to get along with one another. Considering the amount of rigorous psychological testing the early Mercury astronauts underwent just to orbit the earth, it's rather bizarre.