Recently I have noticed an occasional waft of some strange gas or smoke in the cab of my 2002 TJ wagon. It is odourless, and seems to come from somewhere under the driver side dash. Is this likely to be from a faulty A/C system? Or could something else be causing it?

Could it be coolant leaking from the heater and evaporating? - that gives a sweet sickly smell.

Bent. I wonder if it's simply steam coming in from the air inlet? When do you see it? What's happening at the time (eg Air Con off, on, control to floor, wet etc)?

A/C was off. It stopped when the car stopped at the lights and came back when we were going again. It wasn't raining. It did look similar to steam, now that you mention it.

Any mods to your air intake? eg: pod filter, open air box. I too have experienced this in one of my previous cars. It cld be 2 things;
1.Coolant leaking from the heater and evaporating as described above. A known TJ problem with some models more than others. (Look behind your dash for green SH*T.)
2.Coolant leaking/Oil from engine and coming through air inlet.
3.AC is faulty/leaking gas which is usually more noticeable when front demister is on.

My wife has told me that the windows fog up more than usual, and they smear when you wipe them. From my googling, this seems to be indicative of a heater core failure.

Is it safe enough to drive like this? How urgently will this need to be fixed?

Spoke to my mechanic this morning... its a common problem thing with the TJ model. Just gets annoying cleaning your window. ;)

If your heater core is leaking, it will need to be either removed from the cooling system loop (suggested temporary fix) or replaced.
I have not personally replaced one on a magna but from what I have read on the forums here, it requires the dash to be removed to access.
From pictures I have seen, coolant leaks onto the main ecu under it and can cause it to fail, resulting in the car breaking down.