ungrounded outlets

Home built in 1949. Addition in 2005 Original house section had 2 prong outlets and were changed to 3 prong but no ground as original wiring was not changed from 12/2 or 14/2. During addition renovation the elec panel was upgraded to 100amp and is done properly. there is house ground coming to the panel from that section of the house and all looks well there. Since the original part of the house was left alone is the ungrounded outlets an issue?

Grounding type receptacles are required to be grounded.

The receptacles should have been replaced with non-grounding type receptacles, or GFCI protected receptacles and labeled appropriately.

Thanks Jeff

What is the wiring method of these existing circuits? NM cable, AC cable?