It's an interesting suggestion, though there is the problem of fake check ins. You can easily put yourself into a location you're not in or say you're watching a movie you're not. For studios to trust the concept, these apps would require some means to prove you're telling the truth. Meanwhile, moviegoers can already be rewarded for being loyal if not necessarily frequent moviegoers by theater chain clubs like the Regal Crown Club. Every few movies you see you get a free popcorn, see a few more and you get a free pass for the next visit. And yes, some studios get in on those clubs by allowing more points to be given to moviegoers buying tickets for their new film.
As for the prizes awarded for such check-ins, I think it would have to be much better than swag like a t-shirt, poster or some similar marketing tool that's more a benefit to the studios to hand out than it is for you to have it. Anyway, swag like that has traditionally been given out at theaters. How about entry into a sweepstakes for a trip to Hollywood to tour the studio? Or a set visit? Runner ups get free movie tickets? But is there any studio that you'd be that loyal to so frequently? Look at those recent Universal titles mentioned above. Very different kinds of movies.
It's also worth recognizing a comment made to the Ad Age article from the president of Studio Direct, a company that does many things to "make going to the movies better." He says he's working on tests with two studios at the moment on something like what Thilk proposes. I wonder if it's the feature mentioned on the Studio Direct website involving sending feedback to studios and theater owners and getting sneak preview invites out of the correspondence. Would something like that interest you?