I think it's dated campiness is part of the charm. Don't watch it expecting the kind of depth or drama you'd find in the best of today's TV, watch it for the cartoonish space adventure it is.
IMO it's The Next Generation that's aged the worst - I couldn't make it through my last attempt at a rewatch. Awful direction (they stand around, arms at sides like mannequins, taking turns to recite lines), zero excitement and endless prentious, self-congratulatory nonsense. Bleh.