It can be challenging to keep up with constant Youtube+HTML5 updates.
What OS are you running(if not sure, click on the Apple menu then hit "about this Mac") and is it up to date?
I use both Safari and Firefox, with Firefox as my main OS. I even have Chrome installed and fire it up occasionally, although I don't like Chrome as a general rule. Sometimes, websites are glitchy in one browser and fine in another, although there again you have to keep individual browsers up to date too(Software Update handles Safari, while Firefox handles its own updates).