The system does not award points when we think you're a bit far from where you're checking in. You can click on the "Details" tab of the venue screen in your phone to see where we've placed the pin on the map, and if it's off, you can tap the square with the arrow in the upper right corner, and flag the address as incorrect. If you've been checking in more times that we think you can actually go places (remember, no drive-by or walk-by check-ins!), then we won't award points.
You can see all of the badges that you've earned on your profile page at foursquare.com. The badges that display on your phone are only ones earned in the city where you currently are.