Lot's of other F1 YouTube Channels have embedding and sharing enabled. This would allow you to post videos and playlists without unlawfully uploading, claiming to own or illegally sharing.
I would suggest setting up some playlists on YouTube with legally sourced contents and then posting updates to each through dedicated blog-style forums.
Some themes to kick-off with might be "Advertisements", "Promotional Events", "F1-Tech", "Nostalgia", etc.
You could also run a newsfeed with links to other online video content, such as the official FOM videos and BBC videos such as the recent documentaries.
I haven't given this a great deal of thought, but I reckon it will be of interest to a fair few users.
Might also be worth doing something around audio. I was thinking of creating a playlist on Spotify/Last.fm with the playout tunes to all the races this year. Podcast feeds are easy to come by too and are, by their very nature, syndicated.