As others have stated numerous time in other threads about youtube:
You tube videos are in flash.
At this time Blackberry smartphones are not Flash compatable.
Currently the youtube videos the storm recieves are those that are rendered into the mobile format for screens much smaller than those of the storm. this si why the picture is horrible
Yes this should be in 3rd party apps, but as long as we are here ... try free app Vision for YouTube. It loads slower than the YouTube Mobile site but the videos are maximized for quality. Less compression, full-screen. Find it by searching the 3rd Party Apss Forum.