Interesting. I've never even installed Firefox on this machine (Macbook Air, running Lion with Server/ Mac OS X 10.7.2), and I seem to have a version of "the problem", at least for a while. Safari version is 5.1.2. My Quicktime plugin version is 7.7.1.
I started off by visiting a site (http://www.sharperpencil.com.au/work_tv.html) and clicking on the various video links there. I was initially confronted with Quicktime logos and informed that I needed to install Quicktime to run them. (***?). Huh. So I went and pulled up my 'Installed Plug-ins' tab and verified that I had the Quicktime plugin installed (indeed I did), and then switched back to the tab with the links, and lo and behold, the videos were there. O-kay. Repeated the experiment with the next group of videos (there are 3 'groups' of three videos each there), and the same thing happened. O-kay. Tried it one more time, and... a couple of the vids were loading for me, the third wasn't loading (initially) and displayed the Quicktime logo with the question mark in it. In the meantime, the first vids that I'd initially had problems with continued to work fine.
So in my case...
1. There seems to be some sort of cacheing involved - once a vid is available/visible, it seems to stay that way.
2. Since I don't even have Firefox installed and still was having a variant of 'the problem', blaming this issue entirely on Firefox seems to be inappropriate. Not to say that Firefox might not be involved for some people somewhere, some of the time.
3. I'm not sure if I just needed to be more patient and wait a bit longer, or just needed to switch to 'any' other tab and then switch back to trigger 'the right thing' to happen, or if there was some magic about looking specifically at the 'Installed Plug-ins' page to trigger 'the right thing' to happen, but apparently one of those situations applied, and was sufficient (in my case) to Make Things Work.
4. For what it's worth, my firewall is turned on, and all sharing services are blocked.
Hope this report helps somebody somewhere.