The science behind the premise of the show definitely wouldn't stand up but many of the elements of the show, like the Eagle landers, I think would still work just as well today as they did then.
Personally I'm kind of partial to the 70's style sci-fi aesthetics of shows like Space:1999 so I wouldn't have any problem with a reboot having the same look & feel to it but with modern science based story lines.
possible scenario; science geeks on the moonbase figure how to transverse wormholes and next thing they know they do that unintentionally (or maybe one goes psycho and pulls the switch). so they start doing wormholes hoping one will take them home.
not sure how they propel the moon. maybe instead of on the moon its more a space station.
possible cast; Billy Zane as the commander; Kristy Swanson as the doctor / female lead; Rainn Wilson as the chief engineer / tech guy.
A modern, rational Space 1999 story is Alastair Reynold's Pushing Ice. Instead of the moon and a moon base, it is a huge mining ship and a fast moving asteroid that's inertialess acceleration the crew doesn't notice until it is too late.
SF production design between 1968 and 1990 is simply outstanding. The Eagle lander variations, the space suits, weapons and even uniforms are thoughtful and rich. The problem was the plot, physics and aliens. Keep the aesthetics, basic background story and main characters - replace the plots, paranormal nonsense and bad aliens. The basic Swiss Family Robinson theme is a good one with a great look.