I have issues too, but a little different...
I can authorise the app on my iphone to use twitter, and it works for each log, but I need to authorise it every single time - despite checking the 'remember me' box, it never does.
I have just tried to authorise twitter through the website, and while it accepts my username and password, it does not register as connected when I am returned to my profile page.
Any help would be greatly appreciated. Thanks!