I had a plan to buy a mirror lens as a cheapish 500mm tele. I'm very glad I didn't. What I did do was buy a x1.4 teleconverter (Kenko) that I can fit to my 70-300 telephoto. The advantages are huge. On a DX camera the x1.4 at 300mm gives me a 635mm equivalent crop compared with 420mm on a 35mm full-frame, full auto-focussing and image-stabilisation, even in poor light, easy handling compared with a bulky manual focus mirror lens, no shiny donut highlight rings, good contrast across the image and the converter will fit other lenses if I wish.
My impression, given the great number of second-hand mirror lenses that show-up on eBay, is that many people are buying a mirror lens and are then being disappointed. Am I disappointed with my Kenko Teleconverter? Oh no....
I've not tried any 'astro-photography' but I can't see why a mirror lens would have any advantage over a normal lens. Maybe people think that because it looks like a reflex telescope it's better fitted to the job?