1. The term "unit" was a bit confusing to me at first. Normally when I've seen it before it means something that is equal to 1 in some way, such as the unit circle or a unit vector, but here it means something that has a multiplicative inverse (so that, for example, every nonzero element of R is a unit).
2. I thought it was really cool that every finite integral domain is a field. That's a result I never would have expected, and it's a bit mind-boggling to think that Axiom 11 implies Axiom 12 in the finite case but not the infinite one.
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