Obviously the main topic from the original - forced euthanasia for anyone over 30.
But there were others touched upon in the original that have seen a lot of evolution over time (in one direction or another) in our real world since the time of the film...
Such as: plastic surgery, youth culture, ageism, a self-contained & isolated society, wave powered energy, religion, a sexually free & promiscuous culture, social media & on-line shopping (where in Logan's world you could order up anyone who put themselves on the "circuit" - a.k.a. the net - for sex), law enforcement, underground revolutionaries, runaway technology ("Box"), cloning, a non-parental society where children are raised by the state (that one really has some recent relevance), and a load of various political issues concerning freedoms.
I was thinking of how I would re-envision
Logan's Run if I was the script writer/director. And I would do more! By that I mean I'd explore more of the concepts and ideas that were merely touched upon in the movie, like you just said!
First....in the movie people at 30 went to Carousel and hoped to be one of the those who were lucky enough to be renewed (reborn). In the movie no one seems to doubt this concept, except Logan. I'd have a society deeply divided between the devout believers in renewal and those (anti establishment- runners) who believed Carousel was mere euthanasia. I'd make that the focus of the film and show the turmoil it causes the society as this anti Carousel idea grows. We'd see a society that's about to crumble and lose it's techno-perks due to the growing belief that society has lied to the people.
Second....I'd explore what takes place in the section of the city that houses those who live outside of the norm. I believe they were called
cubs? I'd explain them as genetically inferior people
(but only from the elitist city dwellers viewpoint). These outcast live out a normal life span and in doing so achieve a mature and wisdom that the self serving, spoiled rich of the main city never achieve. The
cubs have means to infiltrate the city and can pass themselves off as dome dwellers. They support dissension against a life of consumerism and self absorb-ness that the humans in the main domes have embraced.
Third....under the city and unknown to the people, are the techno-mechanisms in which food is created to feed the masses above. Below the city is a living hell where fish and food from the sea is mass produced by cloning technology and kept in inhumane tanks until killed and processed for protein. This underworld would be a good place to put an updated
Box in.
Outside of the sealed domes is supposedly an ecological catastrophe where an engineered virus destroys any life that comes in contact with it. Thus anyone becoming a Runner and hoping to leave the city is terminated by a Sandman before they can escape....The rub is that outside of the domes the world has healed itself and no one needs to die at 30. That truth would be revealed in the ending by Logan.