Is it unsafe if some three prong outlets don't properly test as grounded?
If an outlet has a ground terminal, it should be grounded.  No ifs or buts.  (And IMO, giving the illusion of ground protection is even worse than not having any protection.).  I don't think you can even get two-prong outlets any more, so I think you'll have to fix the wiring.  It sounds like you're still negotiating, so this is a good bargaining point.  And if you don't get it fixed now, when it comes time to sell, any potential buyers would be within their rights to make you fix it then.

An easy way to check that your wiring has a ground conductor is to open up the service panel, look for the breaker that controls those outlets, then trace the black-shielded wire to where the cable feeds into the panel.  (If it's present, ground is unshielded.)

If you have grounded wiring at the service panel, the next thing to check would be to look inside the outlets in question to see if the wiring there is grounded (it may just be a loose connection, and since it's common to daisy-chain outlets in a room, one faulty wire could affect several outlets).

If you have don't have ground at the outlets, but did at the service panel, you probably have a junction box joining the older ungrounded wiring and newer grounded wiring.  Time to go exploring in the attic or crawl-space / basement.

GFCIs detect a difference between current going out on the live terminal and current coming in on the neutral terminal.  If you're the easiest path to ground in an electrical fault, a GFCI will detect that and break the circuit; without a GFCI, you'd have to hope that you draw enough current -- and for long enough -- to trip a regular circuit breaker.  On the whole, though, I'd rather that current was running to ground through some copper that's intended for just that purpose.