According to user-submitted posts over at both Apple Support Communities and Google Product forums, an unknown portion of Mac owners who run Yosemite are having issues playing certain YouTube videos, with some getting Safari crashes when attempting to watch a clip.
It seems to affect some, not all, HTML5 videos and does not manifest itself when using the resource-hog Flash Player, causing Safari to fall back to Flash for video delivery.
Other browsers are unaffected by the annoying problem. Neither Apple nor Google have commented on the matter yet. Digging deeper, it would seem the hiccup could be traced to the YouTube backend because HTML5 videos in Google Chrome and other browsers play without a problem.