Firefox has a bunch of plugins to download streamed video (like YouTube) but Safari does not.
To download a YouTube video, browse to the video with Safari and hit
Cmd+Alt+A ; this will pop the Activity windows up. Look for a file that’s more that 1MB ; this should be the video file. Double-click the link and wait for Safari to complete the download.
When it’s done, juste open the downloaded file with QuickTime/Perian or VLC.