A lote of sitesuse the Flash version of YourTube. no iOS devices support flash. The you have to either use the YourTube app or Safari to go to YouTube since Safari tells the YouTube site to use HTML5.
For other problems withwith Safari try going to Settins>Safari and clear Histor, Cookies and Data.
Also reset the iPod. Nothing is lost.
Reset iPod touch: Hold down the On/Off button and the Home button at the same time for at
least ten seconds, until the Apple logo appears.