Most people would advise against a mirror lenses due to its fixed aperture which tend to be around f 8 or f 5 or thereabouts depending on model, and the fixed aperture leaves less choice of exposure controls, that being, if subject is bit darker, your shutter speed will be lower, but you can't open up the aperture to let in more light to get little faster shutter speed, as you're stuck with the same aperture. Most people will advise against mirror lenses due to the way the mirror works leaving most background lights as donut shapes and also due to the fact that they don't work with AF so you have to manual focus them,
but...
The point is they were designed to be lighter and shorter, often helpful in some cases where a proper long telephoto lens is too heavy and bulky. An example would be that if you enjoy going for a walk over hills and take landscape photos which tend to favour wide-angle lenses more than telephoto lenses, but if you wanted a telephoto lens in case you spot anything interesting too far away, you would find the mirror lenses a benefit due to their lenght and weight in your camera bag than a heavy and longer telephoto lenses.
The fixed aperture problem that leaves you with limited choices of shutter speeds is actually not really a big problem, as the digital camera's ability to change ISO settings to a higher one anytime you want makes up for it.
It can be of use if you are on a tight budget as mirror lens tend to be cheaper than telephoto lens.
As for the donut effects, they are not always an annoyment, if you frame the subject right, depending on subject and background, sometimes the donut effects can be of creative art.