Fuzzy black border only visible on certain mosaic dataset overview levels.

[MDB_GIS]

Here is a screenshot showing the issue:

When I first loaded the imagery into the mosaic and built overviews, there was a massive black box around the entire dataset. I got rid of that by going into the mosaic dataset properties and changing the NoData Values to 0,0,0. The solid black border disappeared, but this area remains. It only shows at overviews zoomed out beyond 1:52k. Once you zoom in, they disappear completely, so it seems to be a problem specific to the higher level overviews. 

[AmberGuidry]

In order to get these to completely disappear, you will need to edit the vertices of the boundary to ensure that all the black NoData is cropped out. Then go to the mosaic dataset in the catalog pane, right click, go to properties, defaults, and check "always clip mosaic dataset to it's boundary", then hit OK. 

In my experience this has worked flawlessly for me when dealing with nodata. Let me know if this helps

[MDB_GIS]

This is very helpful information and I will definitely have to keep it in mind in the future! Fortunately, I have since solved my issue in another way. It turns out, the black border was being caused because our aerial imagery supplier had included a low resolution countywide preview image that had the no data space as solid black. I was able to correct it by removing that image from the mosaic dataset and rebuilding the overviews!