This formerly solved problem returned the week of September 15:
It's appears that Twitter are experiencing issues with the login process.
The login is actually handled completely by Twitter - you tap login, and you are then taken to a Twitter page, enter your login and password, and they should then log you in and hand you back, already logged in. The error Twitter are experiencing appears to be causing the login to either not respond or the "you are being redirected" message appears.
Hopefully it will be fixed soon and you will be able to log in to TweetCaster
We sincerely apologize for the inconvenience.