Can you please provide example urls for videos to further investigate why this might be happening. Thank you.

YouTube now mostly serves Firefox users an HTML5 player, but the right-click context menu allows you to distinguish the two. If you right-click the green player, can you confirm it is Flash?

If so, it sounds like a longstanding problem with a simple workaround: right-click the media and choose Settings, then the first mini-tab and uncheck the box to use hardware acceleration

More information in this support article from Adobe: http://helpx.adobe.com/flash-player/kb/video-playback-issues.html#main_Solve_video_playback_issues

Any improvement?