It sounds like you have already tried building the overlays, which does usually help if with strange behavior at different scales (ie sometime checkerboard patterns, etc). If you haven’t already looked at these links, they may offer some solutions
How To: Remove black or white borders from rasters in a mosaic dataset
Workflow to clip borders, compress, geo-reference, mosaic aerial photos?
mosaic of geotiffs and remove borders
Edit: a few more link. I know that the check board isn’t your issue, but the solution may be similar...so not ruling out.
How to fix the checkerboard pattern in Mosaic Datasets This fix is if the path changed, ie broken links to source files
https://community.esri.com/thread/189456-build-overviews-for-a-mosaic-generates-blackwhile-tiles
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On another note, as Curtis suggested, it would help others find your question...and help others in the future... if you could edit your title with a short description,such as “issue with borders at different scales of mosaic dataset” or something similar. If you are not sure how to edit the title, one of the moderators would be able to help.