As a general rule, I personally wouldn't transfer anything porous from one plant to the next, especially anything that's been in contact with the roots or have had roots "etched" onto it (clay pots). It's too easy to spread contagion that way.
I don't know how expensive the stuff is you're using, but if that's an issue and the media is clay or porcelain based, soaking for several hours in clear water, rinsing, then soaking again and rinsing should leach out most of the salts or fertilizer.
After that, *bake the media* in your oven for an hour at as high a temp as you can to kill any pathogens!
Somewhat of a hassle, I know, so if the medium is inexpensive enough, I'd just use fresh....