Are you seeing an "Unauthorized" error message when trying to sign in?
Check to make sure that you are using the official Twitter for Windows Phone app and not a 3rd party app (like HTC Peep).
Are you seeing an "Invalid username and Password" error when you try to sign in?
This is likely caused by incorrect timezone settings or an outdated version of the Twitter client application.
If you are experiencing this issue please make sure your Twitter client is up to date with the latest version. Then, check to make sure the date, time, and timezone settings are set to automatic on your Windows Phone:
Go to Settings > System > Date & Time
Tap Set Automatically to ON. Ensure that your settings are accurate and consistent with your current time zone.
Other things to try:
If you are still having issues, please try clearing your device’s cache. You can do this by going to the Settings menu and selecting Applications > Internet Explorer > Delete History.