It's not an error. I've heard it's becoming more popular to use the lunate sigma since it avoids the issue of having two forms of the same letter. Supposedly it derives from some ancient variant of the alphabet, but was popularized more in the middle ages, I think. I'm sure someone here has more details.
I started learning with that book and thought it was weird, but got used to it and wrote out all my flash cards using it. But once I started reading other things, I started to get annoyed with it, so now I've gone over to σ and ς.