Can the issue be reproduced consistenttly ?
One thing you can do is find a situation that is fully repeatable, and then proceed to rule out the irrelevant factors.
For example: shoot with a tripod, using only one lens, then vary the shutter speed (and shutter type such as electronic versus mechanical), and aperture, ISO, etc. Vary the lens, but shoot otherwise identically.
Do the simplest post-processing possible. Shoot RAW so that you can rule-out the JPG engine, etc. Try to determine if it's the lens or the sensor or the subject... etc.