Unless you are a licensed electrician there is no reason to expect you to be aware of a problem with the outlets. I would leave well enough alone. Do not put anything in writing about this matter? But you already did. The following suggestion will solve your concern if you are using appliances with a three prong plug without a properly grounded receptacle. Purchase as many of these GFCI's and adapters you will need:
and one of these for each of the above:
Plug the GFCI into the existing receptacle two prong or three prong and the adapter into the GFCI if the appliance plug is three prong. You are protected.
You might want to warn your land lord friend about the issue because there is the potential of lawsuit if a future tenant is electrocuted.