I think Yelp is missing proof of identity and proof of patronage. It was created before social media took off, and before you could reliably know if someone had been somewhere.
I don't know if you need both, but proof of patronage alone might not be enough to trust a review (See Amazon verified purchases).
Maybe. It still wouldn't be foolproof - after all, Yelp Check-ins are powered by an API that trusts the coordinates it receives.
It might be possible to craft a request for that API. And even using a legitimate copy of the Yelp app to make requests, a jailbroken iPhone can change its coordinates to whatever you want. An Android doesn't even need that - just set it to developer mode and you're ready to fake check-ins all day.
Is that much different than what Facebook or Google Maps are already doing behind the scenes? They might not make that data accessible to you, but it's undoubtedly being (or able to be) compiled behind the scenes. See this update:
I don't know if you need both, but proof of patronage alone might not be enough to trust a review (See Amazon verified purchases).