What do you think the Adobe Flash install does except copy files (to the wrong place)?
I used to have this problem consistently with some site where flash videos would play for a couple of seconds and then stop. I couldn't fix it until I moved the DLL manually, and hunting on the web showed there are a heck of a lot of people who have this problem, and a lot of different solutions which may (but probably won't work).
My system stubbornly refused to work permanently with any of these fixes until I tried moving the plugin to the FF plugin directory, as I vague remembered it being in there before a clean install. You've got a solution to try if you want it to work properly, but if you prefer to keep it broken...
The Adobe Flash plugin has been problematic in Firefox on and off for years. Adobe should install the flash plugin into the Firefox plugins folder where it is supposed to go (and where they used to install it for Mozilla), not just slap it into system32 and hope the system picks it up.
