Thanks for your quick response with this update. I will assume the other plugin isn't involved for now. I have just re-run some tests using MLA 1.70 and both WP 3.8 and 3.5.2; Featured Image is working on my test system.
Just to confirm - are you using MLA v1.70 and WordPress v3.8?
When you say "the overlay comes up empty of content", I understand that to mean you get the Media Manager Modal Window with all the menus and the toolbar, but nothing shows up in the Thumbnails area at the center of the screen; is that right?
Do the "Create Gallery" and "Insert Media" menu selections have the same problem, or is it specific to "Set Featured Image"?
Are the "Show All Dates" and "All Att. Categories" (if present) dropdown boxes populated? What happens if you pick a year/month value that you know has some images? What about other Media Types values?
What happens if you go to the Settings/Media Library Assistant General tab, scroll down, uncheck the "Enable Media Manager Enhancements" checkbox, then scroll down and click the "Save Changes" button? Does disabling the MLA enhancements restore the Featured Image functionality?
Thanks for taking the time to run these additional tests. Unless I can reproduce the issue on my test system there's not much else I can do yet.