Start Firefox in Safe Mode to check if one of the extensions (Firefox/Tools > Add-ons > Extensions) or if hardware acceleration is causing the problem.

• Switch to the DEFAULT theme: Firefox/Tools > Add-ons > Appearance
• Do NOT click the Reset button on the Safe Mode start window

• https://support.mozilla.org/kb/Safe+Mode
• https://support.mozilla.org/kb/Troubleshooting+extensions+and+themes

You can check for problems with current Shockwave Flash plugin versions and try this:

• check for updates for your graphics drive drivers
  https://support.mozilla.org/kb/upgrade-graphics-drivers-use-hardware-acceleration
• disable protected mode in the Flash plugin (Flash 11.3+ on Windows Vista and later)
• disable hardware acceleration in the Flash plugin

See also:

• http://kb.mozillazine.org/Flash#Troubleshooting

Some added toolbar and anti-virus add-ons are known to cause Firefox issues. Disable All of them.

FredMcD said

Some added toolbar and anti-virus add-ons are known to cause Firefox issues. Disable All of them.

It appears an add-on was the culprit here, namely, OpenH264. Once I disabled it, the video problems went away. This was not an add-on I introduced to my browser, it comes, evidently, with V34 &V35.

Good work. Well done.