I solved the problems people have been dealing with in your plugin. The fix comes down to wordpress having issues with HTTPS requests and not having a valid CA cert, a missing parameter in the access_token as well as a missed URL update for the callback to verify the account login.
I did this by:
--Updating OAuth.php to the latest and adding your class_exists check back in.
--Change the $TO_API_ROOT variable to use http:// instead of https:// in twitterOAuth.php
--Update the $this->accessTokenURL() to accept a required parameter $_REQUEST['oauth_verifier] in twitterOAuth.php
--Update the function stc_get_credentials() to use "http://api.twitter.com/1.1/account/verify_credentials" as the url for the stc_do_request() call in stc.php