I would say one of the biggest issues these days is the limitation of the FMC with regards to coding of 1/2 degree RLatSM NAT tracks. That is what would most likely cause a GNE these days. Strict adherence to a MNPS/NAT HLA checklist should prevent this as well as the CONFIRM ASSIGNED ROUTE UM. It won't be long before CODLC and ADS-C will be required in all NAT HLA so you will be informed of any tracking error before you can work it out from the plotting chart.
Saying that, the plotting chart does help increase SA and would be helpful during certain aircraft systems failures.