Using Twitter for SEO and SEM
The thought of using Twitter to give you an SEO and SEM boost is appealing, but not so clear cut. Yes, you can place links in Twitter tweets, but since Twitter using the "nofollow" attribute, Google will not count such "tweet links" as inbound links to your own web pages.
That is the bad news.
The good news is that Twitter tweets are a good way to drive traffic to your web pages. After all, the whole point of achieving a high placement in Google search results is to get users to click and navigate to your web pages.
Twitter has a search feature where people can enter keywords to search for tweets, so be sure that your tweets are rich with the keywords that are likely to be used by your target market. As far as I know, the search results are strictly chronologically ordered, so there is no Google-style SEO to do other than to use lots of keywords.
As far as the issue of Twitter using TinyURL links, that is a non-issue due to Twitter using "nofollow".
I do not have any great clarity as to whether the existence of any of your URLs at TinyURL.com actually gives your URLs some SEO boost. I suspect it might, but it is hard to say for sure. I suppose it can't hurt to enter your important web page URLs into TinyURL.com, treating it as if it were another form of web directory.