Sorry I couldn't help.
For Bill's old Samsung Galaxy Tab 10.2, with auto-updates turned off in everything that allows that (OS and Firefox), embedded YT vids still work fine here on ES as of today.
I don't know what versions of Flash, FIrefox, or Android his old tablet is running though, I have to find out.
Haven't heard yet whether or not his android phone works with them or not, or his PC.
But since they do still work on the tablet, that means it isn't a change at the forum end that caused it, which at least eliminates that as the cause.
A few possibilities exist:
--Something in Flash itself was changed to require different scripting to tell it how to play as an embedded Flash file, so that anything with the newer Flash wouldn't understand the commands from the PHPBB page. This possibility only works out if everyone with the problem has had Flash updated (automatically or manually) on all of the problem computers, since the last time that it worked.
This can be verified by reverting to older Flash versions and seeing if the system now works. Sometimes reversion doesn't cleanly occur, and manual cleanup and reinstall would be needed; depends on the system and the design of the uninstaller.
--Something at Youtube's end was changed to require different scripting. This possibility isn't likely, simply because it still works on some unchanged browsers (like Bill's old tablet).
I'm not sure of a way to specifically verify this, since it's unlikely YT would respond to any questions about this (why would they care?).
--Something in the browsers themselves was changed to produce different rendered results for the PHPBB-generated pages. This possibility only works if any browser that was verified "broken" was updated on all of teh problem computers since it last worked.
This can be verified by reverting to older browser versions taht worked; same caveats apply as with the Flash reversion.
--OS update to some critical DLL / etc file that's commonly used by whatever is doing the rendering or interpretation; seems unlikely simply because of the wide range of different OSs that exhibit the problem, but there are so many dependencies between things I suppose it could be possible anyway.
This could also be verified by reversion to previous state when system was known to work, and same caveats apply as with other reversions.
--Something different is causing the problem in some of the computers vs others. This would make it much harder to nail down the issue. I don't know of any certain way to verify this type of cause, other than for each person to fix their own issue and report what was done, and find that each fix was different in what it would do to their system.
--Any other ideas for possible problems?
FWIW, there are a lot of hits on Google for this general type of problem, going back a ways, like this one:
https://support.mozilla.org/en-US/questions/981145
A few I saw pointed to this
https://support.mozilla.org/en-US/kb/mixed-content-blocking-firefox
which may apply to other browsers, too, especially here on ES because it does use HTTPS:.
One possible search of many
https://www.google.com/search?q=All+embeds+from+utube+are+just+black%2C+t&ie=utf-8&oe=utf-8
another
https://www.google.com/search?q=youtube+embed+black&ie=utf-8&oe=utf-8