As mutt7469 said, we don't currently support SSO via mobile.
The sign-up process on foursquare always results in the creation of a foursquare password (even if connecting with facebook). We support logging in to the website via facebook, but from the mobile applications you have to specify your foursquare account identifier (generally your phone number or twitter handle) + foursquare password
~ak
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Akshay Patil / Foursquare Platform Evangelist
@akdotcom / @foursquareapi