This may be a daft question, but if a tweet has a link to a site, does this count as a backlink or just a social mention?
Also if this link is done through bitly or similar does Google still see it as a backlink?
Some times it do but you need to have a really strong community of followers some one the websites that i am working on when i check there back links they do have twitter back links mentioned in that.
Twitter can give you some backlinks, but your better off building up your following base and driving traffic to your site that way.
If your short link is a 301 redirect to your site (which bit.ly supports), search engines count that as a permanent redirect, and will count it as a backlink. If its a 302 redirect, search engines assume the short url is the target url which is being redirected to the linked page temporarily.
Twitter links, as far as my knowledge is concerned, are no follow links and according to some no follow links are also good for seo.