Pros
First of all, the opportunity to live and work in so many different schools around the world. They offer an internal transfer system making it easy to move between locations. All IH schools are different, but in my experience they really take into account the wishes and desires of every employee (class level preferences, for example). I like the flexibility of your working week - schedules and classes can change often - adding an element of variety to your timetable. Most of the students, especially the adults, are generally motivated and a pleasure to teach. And of course, in this type of environment, you're surrounded by like-minded people with similar philosophies and interests.
Cons
As with most English teaching positions, the salaries aren't the best, especially in places like Eastern Europe, where demand is exceptionally high. You do get decent holiday time and minimal local benefits (medical, etc) but their standards can vary. Although most students tend to be motivated, like many language schools, there are a handful of bad apples, usually grumpy and irritable teenagers. If you don't like having such a flexible timetable and prefer more stability, it can be tough. Split shifts are common - class from 9am-11am and then 6pm-8pm. And communication between management and staff isn't always the best. Things and procedures change from time to time and teachers are often the last to hear about it.