As a Foursquare user, I'm often struck by about how much coolness is left at the door. Or maybe it's already happening and I'm just not aware that it's happening. It feels to me, at the places I visit, that they still don't have much of a clue (if any) about Foursquare. And they certainly don't see it as a way to increase regular, repeat visitors. Which is the lifeblood of any successful business, especially restaurants.
But, if I were running Foursquare, I would encourage businesses to put a logo on their door asking people to check-in and suggest they put it on their menus or menuboards as well.
I would also offer a service where each time the mayor changed, they received a fax with the name of the major and the mayor's photo. This could be posted on the wall, or pinned up by the timeclock in the back for all of the employees to see, to keep an eye out for. Imagine walking into a restaurant and hearing "Norm!" (if your name was Norm) because you were the mayor. That would certainly keep you coming back regularly and encourage the other patrons in the restaurant to perk up and check-in.
And I would add "regulars" as a small group of people who aren't quite the mayor, but through some combination of frequency and recency, stood out as people who visited regularly. Maybe they would appear as a small strip of 5-10 profile photos below the mayor on the fax.
And if they don't have it yet, I'd provide badges business owners could put on their website that would show the mayor and the regulars.
And most important of all, I would offer a service that by fax or text message, informed a location when its mayor checked in. (A nice lower-tech options for restaurants that aren't online or don't regularly use the internet.)
And I would think about buying Yelp or starting a competitor. Not quite sure on this last one. Some places still haven't figured out how to use Yelp to their advantage (and there is some concern that Yelp may be trying to strong-arm companies) but you'd think a place as good as this one could flood Yelp with great reviews (we have nearly all positive remarks from our multiple visits) but instead, this is kind of embarrassing.