Full time, and they can go to teams training camps and stuff all spring/summer to be essentially "reffing" year round. They can have down time to do whatever they want that aligns with the players schedules. $200K is a pretty damn good salary, considering its for about 5 months out of the year. And I'm guessing during the season the NFL covers most things like travel, lodging, etc.
The officiating needs to be fixed, but it's really hard to get people interested in doing it. Unlike high school sports or even college, the NFL has the power to get the best of the best and make it a very desirable job to have, even with the scrutiny and pressure that comes with it.