I'll share you my experience.
I've never had any issues with my knees with jumping rope, and I used to skip the rope up to an hour at a time.
I had problems with shin splints, stabbing kind of pain, because I had a bad rope for double-unders (two skips in one jump) so I had to jump higher, and I used to jump bare-footed on hard surfaces (laminate flooring or even concrete).
What is a bad rope for double-unders? It is any slow rope. Mine was fabric, which cannot spin fast enough, and I was motivated to beat it by jumping higher so I had high impacts on each return back to the floor.
These days I use cable jumping rope and wear shoes when skipping and I have no issues whatsoever. Cable is very fast and hard, and the only impact it does is when it slaps my skin on a missed skip.
Just make sure to get a rope that matches your current skills and upgrade when necessary. I've learnt it the harder way. =)