Pros
Stable - short of people abuse or setting the campus on fire, you can pretty rest assured that you won't be laid off or fired. It is a government job. Benefits package is great, and if you're a lifer their retirement benefits are also quite outstanding.
Cons
Related to Pros, but since they can't fire people, you have a lot (A LOT!) of incompetent people working at very high, and mid, levels. People that would not survive a week in a corporate environment before getting fired. Lots of red tape. Throw away any reasonable expectations out the door. Something that in a corporate environment would take 2 hours to a day to get done here it can take upwards of a year. Not kidding about it either. Unless you're tenured faculty the options for growth of staff are somewhat reasonable, but nowhere near great.