I just started a Klingon career, and I could not find anything on it when I did a search for Invisible in the search function of the forums.
When I play ground maps, some times people just disappear myself included. Some times I look into what appears to be an empty hallway when suddenly I am met with a barrage of phaser fire. If I move two steps closer I can see several Feds there very close, if I move two steps back they disappear and it looks like just another hallway again. Are some maps more plagued with this than others, maps to avoid and so on?
Tactical officers (maybe others) can activate a stealth module - essentially a personal cloak. They're are ways of detecting it (I think) but if you can't then you'll have to get use to that guessing game. Personally, I love using the stealth module.
EDIT: Actually, that sounds like a glitch. Never happened to me.