The phrase "apparent inconsistency" means that something seems contradictory or does not make sense, but there may be a logical explanation or a hidden connection that we are not aware of. Full definition
The amendment process would necessarily cause apparent inconsistencies between the ethical confidentiality rule and the privileges to be addressed. (slaw.ca)
Finally, some important apparent inconsistencies noted in the observational record have been largely resolved since the last report. (scientificamerican.com)
The answer to most apparent inconsistencies in religions is that God is omnipotent and therefore immune to the normal rules of logic. (wattsupwiththat.com)