If you have Handcent installed on your Android phone, and messages aren't forwarding to the MightyText Web App:
1 - Launch Handcent app on your Android phone
2 - Under 'Application Settings -> Default Messaging Application' - select "Disable" (Handcent should still work fine on your phone)
3 - Now, see if incoming messages are properly getting forwarded to MightyText Web App
4 - If it doesn't work, restart your phone and see if that fixes the issue
5 - If it still does not work, you should un-install Handcent (temporarily) to confirm that it is indeed the cause.