There are over 400 stat posts on DMR. Browse the full list here.
The Inaugural Service Badge can only be unlocked on the National Day of Service (this Saturday). To unlock the badge, you need to sign up for and volunteer at an official National Day of Service event and check in to it.
Anyone attending the Presidential Inauguration will have a second crack at unlocking the badge. All you have to do is check in to the National Mall on January 21st to earn your Inaugural Service Badge.