If you are hit while dodging as a Fury/Slayer/Cabal or hit while SS'ing as a Shadow you can become invisible. (fixed by dodging in all directions)
To be honest, I'm kind of amazed that I have never experienced this one. That having been said, I never really play the Shadow off-host. It could be that the issue has a correlation with lag, or it could could be that I rarely host anymore, and thus rarely play the Shadow. I have seen invisible teammates before, but there are a few potential causes for that one.
Edit: Yes, I re-read that last sentence, and decided to keep it anyway. Also, it was intentional.
If you are healed while getting shield/healthgated at the same time, you can get stuck in permanent "red death screen" (until you lose shields again)
This one is the bane of my existence as a Shadow (or Volus.) Drives me nuts.
or your powers/guns can stop working (unless you melee)
This one I've only ever had from specifically being shield-boosted. I don't recall ever having it happen from a Geth Turret or a Shadow Strike.
Ohgawd... if that was a side effect of Shadow Strike... I'd have to Heavy Melee right away! 
Which I already do a lot of the time, anyway. 
Okay, it might be possible that I've just never noticed that one, either. 