Just to clarify, when I'm watching a YouTube video in full screen, tapping on the "settings" and "exit full screen" buttons has no effect. My question is how do I restore functionality to these buttons?

Here's a workaround for anyone who might be having the same problem:

To exit full screen view while playing a YouTube video: tap and hold on the screen > drag down and release.

To access the settings while viewing a YouTube video in full screen mode: exit full screen mode using the steps in the previous paragraph > tap on the settings button (gear icon) > make settings changes > tap ok > tap the full screen button to return to full screen view.

Now when it goes into full screen mode the following message is displayed: "To exit full screen, drag from top and press back." In actuality it isn't necessary to perform both of those actions in order to exit full screen mode. The message should say, "To exit full screen, drag from top and release OR tap the back button."

One additional observation/suggestion: Considering the fact that the "restore screen size" button is no longer functional, why not get rid of it? It serves no purpose.

Button functionality has been restored. Reading over my earlier comments it appears that this problem was caused by YouTube and not firefox.