You may (I should say will) see errors in the coding of your database. When you see this, get after the flight technical group at your carrier to correct it. The RNP value for each leg is an insignificant looking, three-character value buried deep in the ARINC 424 procedure record. I always imagine these values being painstakingly created by engineers with massive computers, detailed obstacle surveys, laser theodolites and pocket protectors inside their pocket protectors. Once created, your database provider has some white-haired grandmother, with absolutely no aviation experience (and no clue as to what she is entering), quietly enter the data via a keyboard. Errors are made by one or both parties.
Generally, you are able to run comparison checks between the last database and the new one and any change requires some scrutiny. Obviously, new procedures deserve a complete top to bottom physical so that no errors go undetected.
All that said, if you see an RNP value on the CDU that does not match the value shown on the chart you need to do something.
Eliminate the obvious. Is the FMC on the correct nav cycle (valid dates on the IDENT screen)? Do you have the correct plate? Be especially careful if you are one of those guys that files your approach plates without looking at the effective date. If all that well and truly matches up, then change the RNP value on the CDU to match the plate. Manually entered RNP values display in a different font and cannot be overwritten by the FMS. This means that if you enter a more restrictive RNP for the approach and then miss, as the speed picks up you may run into GPS latency issues and the dreaded UNABLE NAV PERF message may appear.
The Air NZ B737-300 and Qantas B737-800 have been operating RNP AR into Queenstown for three years. Air NZ are using 0.3 and Qantas are using 0.15 both are planning 0.11 approaches.
We use approaches at RNP values of 0.5 all the way down to 0.15. We have a new approach that specifies RNP 0.11 but the cert test flights are not yet complete, so we aren't yet flying it for score. The 737 NG can be certified down to RNP 0.10 but you must specify the NAV PERFORMANCE SCALES option to get that value.