It looks like it could be spider mite or eriophyid mite damage. They're both easy to take care, use a horticultural oil, insecticidal soap, or dormant oil spray. Depending on the temperature outside, the hort. oil may not work but a dormant oil should still kill any eggs this time of year. Whatever product you use, make sure you drench the entire plant especially the undersides of the leaves because this is where they hide. If you're keeping this inside, the eggs may have hatched and this is the new generation. Kill them before they mature and lay new eggs!!! You might have to do a few applications a week or so apart.
I'm also not ruling out a disease. The spots usually indicate a bug problem but on the third picture I noticed some bare twig tips, this could indicate Phytophthora, Volutella, or Cylindrocladium (Boxwood blight). The dead tips could also just be desiccation...
Good luck!