Consider using the first letter of the current status of a boards, permission's settings? This way we can see at a quick glance if the permissions are set correctly. This would save us a lot of work from having to dive-in and look at each boards settings.
Here is an example I created for clarity. My suggestion is in red:
After all that work, it would really help seeing it there then I could tweak the one or two that I may have missed.
When you hover over a list item, you'll see several icons on the right side. If you hover over the icon that looks like this: , a tooltip will appear after a moment or two which includes some permissions information.
EDIT: After further investigation, I discovered the only permission being displayed is the 'Who can Access' for the category and board. This isn't enough to suit your needs.
That isn't an "at a glance" method like your proposal. But for now, it would be faster way to check than clicking the icon and selecting the properties tab.