What version of Adobe Flash flayer have you installed? Open system Preferences->Flash player and see if it finds an update. Plus if that doesn't help go get the Flash Player Uninstaller, log out and then ;log back in and go get the latest Flash Player. See if that helps.
I'll try that soon. First, now it looks like a personal problem - again. I logged into the guest account and the offending video played, with audio, just fine. Perhaps one of my extensions is messing things up.
Well, the problem is gone. I have no idea how/why. I played games with my Safari extensions, but nothing changed anything. Then I uninstalled Perian 1.2.3 - still no audio. I reinstalled Perian. Now I have audio! Maybe something in there got corrupted. Go figure.
I think Perian has been "retired" since the release of Quicktime X. That could have be the problem. However I did discover the /Applications/Utilities/Audio MIDI Setup is almost essential with mine being set to 441000.0 Hz with 2-channel 24bit Integer set since i have only a 2.1 speaker system connected to my Mac Pro.
I was glad to see you trouble shot the problem almost like a pro Mac user.