foursquare's competitor is other mobile 'time wasters'. I mean that in a good way, not bad way. so facebook, twitter, instagram, etc are all competitors.
if you want to talk about check-ins.. check-ins are commodity, i'm sure foursquare knows this. noone says "hmm.. what app to check in??? hmm what competitors to try?" they go "hmm.. what's interesting and fun way to show off and impress others while i'm here in this restaurant? facebook? foursquare? foodspotting?"
To answer your question about who our competitor is, it's the same as it's always been (and always will be): the back button. Our job, as pg says, is to build something people want. We started by building checkins and attracted millions of users doing that, now we're moving on to building the best social city guide we possibly can as well as starting to explore interesting new ways for local merchants to communicate with their customers.
It's not about beating someone else. It's about building something useful enough that people will pay attention at all. That's what startups are really about.