I bet you never knew that Opera had an issue with YouTube. Well I know that I did not, but I am glad to know that it is being fixed as I am writing this.
The issue seems to be with Opera 10.5.1 and has affected a large number of Opera users. The fix was fairly quick from the Opera side as they only ask users to go to Help then check updates. At this point a simple .js file is installed that allows Opera to update web pages on the fly
So if you are using Opera 10.5.1 and are having problems with YouTube, well here it your fix.