Did you download from http://www.mozilla.org/en-US/firefox/new/?

The installer should be signed with a valid signature...

I always download all my updates from the Mozilla website so that definitely wasn't the issue. I double-checked the URL before posting this issue... it didn't happen once, it happened even after I closed and reopened the browser. Very strange.

Tonight I tried again but because I have a Logitech webcam, the update failed to complete. I disabled the webcam and tried again to no avail. What could cause this?

Please attach a screenshot of the dialog you are seeing