In addition to the excellent answer given above by Lucifer, I recommend that people looking to develop or use Libraries, review the following BB supplied KB article:
Working with Libraries - shared, bundled, releasing, and using 3rd Party SDKs
Where the API is available as source or a Jar, I have found it significantly easier to include the source directly in the application. For example, in this case, rather than include the TwitterAPIME jar, you could include the TwitterAPIME source as a separate project in the application. As well as being easier to build, this can help in debugging or at least understanding issues with the API.
You might also find this sample, and in fact the containing Thread, useful:
Twitter + Facebook Sample Integration