I recently re-watched my Logan's Run Blu-Ray disc and thoroughly enjoyed it. In my opinion, it holds up pretty well, and is a highly entertaining 70s sci-fi adventure film.
Sure, there are some logic problems in the script, and some of the effects shots look dated (although, surprisingly, the miniatures of the City of Domes actually look a bit more real in HD instead of less; the only thing that really betrays them is the use of water on the tabletop sets), but there's a lot to like in there, too. Great production design, good cast, and plenty of interesting ideas - even if not all of them make much sense.
Here's the original theatrical trailer.