#Typo #1:

There are two different objects that represent a user in the Stack Exchange API, the full user object and the smaller shallow_user object. Which is returned depends on the method being called, methods that are focused on users return the full object while others return the shallw one.

FIX: In the last sentence, change "shallw" to "shallow".

#Typo #2:

Some badge, like Autobiographer, are held in common across all Stack Exchange site. Others, like most tag badges, very on a site by site basis.

FIX: In the last sentence, change "very" to "vary". Also, change "badge" to "badges".