Parents have a 1950s house in NY; most of the electrical outlets are the old two-prong, ungrounded type. The cable is old romex type with no third wire, so the ground screw of each receptacle is unconnected. When the outlet is tested it comes up 'open ground'. Been this way for years with no incident. Except that nowadays things are done much more safely. (As you all know in even older houses, if the cable is BX, a ground is available from the shielding.)
As the house will be sold in a few years, I asked the electrician about the cost of converting all the outlets, and it's quite expensive. The new owners can certainly deal with this. If I was going to buy a house and knew that I'd have to start chopping almost every wall in the house to put through new lines at signficant cost that might make me hesitate.
What are the potential safety hazards here?(Years ago some electrician must have installed about a dozen 'false' three-way receptacles, which come in handy for certain appliances with the three prongs.) One we can remove the false three-prong receptacles or two we can bring the house up to date or three leave it all alone and let the new owners deal with it.
Note: a number of strategic outlets are grounded but vast majority are not.