There are some situations where MLS will take invalid data coming from CDOL and clean it up for display in MLS. This may result in things appearing correctly in MLS even though there is an issue with data recorded in CDOL. It sounds likely that there is an issue with the data in CDOL that needs to be corrected, but I can't be sure without looking at the actual unit data.
The next version of MLS (3.7.1, coming "Soon") has some major revisions to the CDOL processing code. When MLS processes a full unit data refresh, there are some cases where MLS 3.7.1 will detect data issues and send transactions back to CDOL to correct the issues. We have done some fairly extensive testing on multiple bishopric scenarios. Relief Society presidencies are a little more difficult since having multiple Relief Society presidencies is a valid condition.
In that case, you can either call the service center and have them address it or you can try a refresh with 3.7.1 after it is released and see if that makes a difference. If you want to send me your unit number by PM, I'll run it through as a test case and see if whatever is causing your issue is something we can detect in the refresh processing code and correct.
This isn't a CDOL issue, but just bad data that has gotten into the CDOL database. We have found some creative things that can happen in CDOL data based on weird use cases with MLS.