Saw a few glitches in Ur today who were invisible - just a floating name, I guess it's a bug of some sort. But wouldn't that be cool as a costume? Kudos to Gist and DoctorVeneno for accidentally helping conceive this one.
I think it would be much cooler as a skill, maybe high in the Meditation or Camera branches. Allow you to sneak up on chickens, avoid jujus, and things like that.
An invisibility costume that gave the character a slight distortion to the background behind them would be kind of cool, I think. But yeah, I've seen this happen to others a few times.
Sounds like a loading issue. I've had that happen before on highly crowded maps. I also have the problem of items that take minutes to appear in my house. (Most notably-- my closet takes forever to show up.)