Windows 7: Local Group Policy and Firefox plugins (Flash)

I recently locked down a PC's with LGP. It is heavily restricted for public use.

One strange problem that has cropped up is the Flash player in Firefox.

I didn't install the plug-in before I locked down the user account.
Afterwards I realized I hadn’t installed it so I logged on to the Admin account and installed the plug.
The player now works fine when logged in as Admin or as a User with full privileges but won’t play in my locked down user account, where I still get a message saying the plug-in is not installed.

Any ideas what’s going on here or what I might have done in LGP?

It doesn't work because the LGP is in effect. Since you added Flash after enabling LGP it makes sense. Just like what you wanted. Say you don't want Flash on the computer for security reasons, but someone tries to install it. It won't work. You need admin account to use it. If you want Flash and LGP you need to undo the LGP, install Flash, and then re-enable LGP.