A recent updater for Adobe Flash caused it to fail on certain older Mac models (like my Mid/Late 2007 Macbook Pro). A fix was released within a week, but keep in mind there are alternatives out there for watching YouTube, such as HTML5.
In addition, you should never download a Flash updater from anywhere except Adobe. Not too many years ago there was a trojan horse made to look like a Flash updater file. Only use Adobe's web site, or an established software update site with direct links to Adobe, such as my favorite macupdate.com.
The Mac Doc