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I do quite a few searches on twitter; unfortunately usually there is even more "noise" then even Google shows.

I'm not convinced syndication via other players is the best link building tactic because if anybody links to or embeds them they're linking to the host site and not your site. If the aim is to let people see and talk about the content (as in, if they're likely to do a blog post or otherwise talk about your site with a link when using these videos) then it's not bad, but there will almost definitely be some leakage. So, definitely do it for exposure, especially if you think it's the only way people will see your videos in the first place. Not the worst thing in the world if you're selling something or it's the type of content people blog about. However, if you can host your own player (or something like Brightcove) and have a link back in the player then that's going to be better in terms of link acquisition.

I generally just use Xenu's hyperlink sleuth (if you thousands of pages) to listing out all the URLs you have got and I might then manually take a look at them, however, see the guitar in demand I have not come upon an automatic device yet. If all people are aware of any, I'd like to recognize as properly.