You can watch it online here:
The New York Times has a review. 1000 Misspent Hours gives it some praise but ends with this: "it’s a hell of a lot better than Rollerball." Moria notes "it received an almost universal panning from mainstream critics and genre fans alike," and describes it as
a film that seems like it is made by middle-aged conservatives who can’t understand what youth is rebelling about and believes that what they really need is to forsake hedonism and make a return to traditional respect for one’s elders, for the sanctity of family and marriage and the American flag.
Roger Ebert likes it, saying
is a vast, silly extravaganza that delivers a certain amount of fun, once it stops taking itself seriously.and that it
has wit enough to work on such a level; even while we're chuckling at such an audacious use of cliche, we're having fun.
SciFi.com ends its review with this:
Despite its Oscar, this is not a special effects movie; it is a philosophy and character movie that adroitly uses effects (and action and sex). Though at times campy and problematic, in some ways Logan's Run exemplifies how a science fiction film should be made.
Stomp Tokyo starts with this:
Upon your admission that you've never seen Logan's Run, a friend or family member may turn to you and say: "You've never seen Logan's Run? What do you mean, you've never seen Logan's Run?" It's that sort of movie.