When using the Fix page vs. raw data to check the position-
Regularly seen errors involving the radial from the gound VOR to the aircraft as seen by the FMC due to the aircraft variation database being in error. Can usually predict this one happening if you compare the A/C true heading (from the IRS control panel in HDG/Sts) with its magnetic heading pre flight. Compare this with charted variation. Normally on affected A/C you will see a difference of 2-3deg.
Hardly ever seen errors with DME side of things- 90% come out at within .3nm