OK, so I've got a slimline Acer desktop and there simply isn't room to stick a decent power supply in this thing. Some googling, however, has told me that its apparently ok to run a psu outside the pc's case. I have a few questions, though:
1) Is this, indeed, safe?
2) I've read that grounding is not a concern, as that is provided by the outlet via the third prong. Is this true? If not, what would I have to do to ground the psu?
3) Anything else I need to know? Potential hazards?
It's perfectly safe, and you're correct about the grounding pin (correct me if I'm wrong) so you don't have any worries about shorting.
There are a few potential hazards, however -
1) If your PSU fan is of modern build, it will most likely have a 135MM fan on the bottom/top. If you orient it so the fan is on top, you have the chance of dropping something into the PSU while it's on.
2) This isn't really a concern, but you could get some major dust build up inside your PSU due to it being outside instead of sucking in air through a filtered intake (Not on all cases, but most bottom mounted PSU cases will have a filter)
3) You could knock your PSU off the table/off the top of your case which may cause you some troubles.
Besides that, I don't really see a problem with running a PSU outside your case My brother ran one like that for around two months before getting his new case, didn't have an issue
That's perfectly acceptable as long as you heed mocchan's advice. Many rigs have no case at all. As long as you are plugged into a properly grounded outlet, you won't have any grounding issues to worry about. If your PSU has a fan on the top/bottom, you may want to set the PSU on its side so dust doesn't get sucked into it as much.