I finally got to see this movie. It is excellent. It is well paced, acted and directed. It manages to satirize Hollywood while being a real thriller (even though you know the ending).
It is not history. The movie was fake, The mission was real is true for both their cover story in Iran and this film. Affleck and the writers took some artistic license with the material. It is (in my opinion) too generous to Jimmy Carter. Nevertheless, the basic story is true and Affleck does a great job capturing the era.
Here is the Wired story about the real rescue.