I already wrote that the movie "Logan's Run" should be remade based on my theory of why remake good films when there are so many films that didn't quite make it the first time. Logan's Run was certainly not a complete failure and even spawned its own TV show. Unfortunately, spawned is a good description of the show that is more a curiousity than entertainment.
First off, let it be known that I now clearly nominate "Logan's Run" for having the most irritating music in TV history. It's half disco, half riffing dog barks on a moog. It's all annoying and gets into the back of your head and does horrible damage. It's a musical "Pew, pew, pew" that thinks it is a John Williams score.
The show itself is sort of faithful to the movie but not to the spirit. Logan and Jessica have left the City of Domes (that's the name, obviously in the future there is no imagination.) They are sort of seeking Sanctuary, but really it's an excuse for them to meet a new "society" each week aka the problem of the week. So we don't forget the reason for the show the old men who rule secretly over the young people of the City of Domes sometimes hatch a plot to bring them back so they can brain wash them into model citizens and end all this annoying rebellion.
This is seventies TV at its lowest. The plots scream out the problem of each society with the subtleness of a hammer in a glass factory. Even famed author Harlan Ellison couldn't do too much with his episode and wisely made it into a who done it. The special effects are.... interesting. The only good thing is Donald Moffat who plays the android Rem. He really doesn't belong in this show but he also clearly is having too good a time being Data before Data.
If one needed to remake the TV show for today I'd certainly keep the focus more on Sanctuary. Also, I'd sharpen the focus on Logan and his gun. The Gun in Logan's universe is nearly as important as the ring in Lord of the Ring. It's nearly a religious item and it now belongs to a priest now heretic.