They take on an air of other-worldliness. They get flaky. Their family life often suffers. In church, mundane things like helping in the nursery, giving someone a ride, or cleaning up after meetings is beneath them. Nothing matters except prayer, and they alone have the true anointing to do it.
Some intercessors become spiritually puffed up.
This is the sin that caused Satan to fall from heaven. Lucifer was apparently created as a beautiful archangel with the capacity to make music, to worship, and was designed to be near the throne of God. Intercessors also draw near to the throne of God. Because they spend a lot of time in prayer, they get inside information. This can lead them to think more highly of themselves than they should.