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I have never witnessed, or heard of, any cephalopod getting parasitic infection from other fish in the tank. I may be wrong, but I believe that both Icthyopithrius (sp?) and crytokarion (sp?) are only found in vertebrates. Icthyobodo has been described in octopus (Forsythe et al., 1988) From the literature, the most common problem of captive octopus seems to be bacterial infections. I would not be very alarmed if I observed any fish to be infected in a cephalopod tank. I have a couple good references that I will get to you when I have some more time.
From what I could find, Vibro is the primary infection of concern (also deadly for seahorses) and there is little to nothing that can be done if it appears.
I did add a small amount of tetracycline to Trapper's shrimp when she started to weaken after the babies hatched. I have no clue if this helped her prevent infection in her weakened condition but she never showed any kind of skin problem.
One of the biggies is autophagy disease, but I've never seen it cross to other marine animals or to people (at least none of our aquarists are chewing off their own arms ). The jury is still out on what causes it, stress in some cases seems to play a part but there is also some speculation that a prion (like mad cow disease) is involved. It is HIGHLY contagious to cephs.