I'm still seeing this issue (running Mountain Lion 10.8 and using Xcode 4.4 4F243). I never had this issue using Xcode 4.3.3 on Lion 10.7.
I have tried to "Reset Content and Settings..." from the iOS Simulator (I've used both version 5.0 and 5.1 for iPhone and iPad), but I still get the error "Error Signing In - The user name or password is incorrect". I've also tried turning off OS X date and time setting and back on to use Apple's time servers and restarting the iOS Simulator.
1. Run iOS Simulator (using Hardware Device iPhone, Version 5.1 9B176)
2. Go to Settings / Twitter and enter my user name and password (the same combination works in Safari and I can successfully log in to Twitter.com)
3. Click the Sign In button
I still get "Error Signing In - The user name or password is incorrect".
Got any other other suggestions or solutions?