There are two quality checks. One is performed by scripts developed by Phil Gladstone. This is the main QC on CWOP data. However, data is not thrown out because of this analysis' results. This was just something a private individual did on his own time, on his own equipment, as a service to CWOP members. Its sole use is to give CWOP stations a heads up on the possibility of a problem with their sensors. Determining whether there is or isn't an actual problem is entirely up to the CWOP member.
The second quality check is performed by the MADIS system after the CWOP data is ingested. This is something that is applied to all ingested data. There are many data networks that feed into MADIS, of which CWOP is just one of many. There is publicly available information on the various checks MADIS performs. These checks are performed against individual data points for every station. Consumers (which means various NWS and University computer programs) can use the MADIS QC results to filter data they utilize. In general, data has to be very whacked out to get flagged by MADIS.
The quality checks are just computer algorithms that munge data. They are not meant to be taken as personal insults of station owners.
As for the APRS/CWOP connection, there is not a lot of connection anymore. Non-HAM CWOP members send data directly to servers set up specifically for non-HAM CWOP members. HAM users submit to APRS servers that no longer accept data from non-HAM CWOP folks. The only thing in common is the specification for the data packet structure.