Decim didn't see the woman's expression when she started lying at the end. All he saw was her insane behavior. The assistant had a critical edge.
Even then, Nona clearly said that Decim was not wrong. He should not be swayed by momentary emotions. The woman may have wanted to save her husband at the end, but that does not erase the fact that she had an affair, an act that would destroy her distrustful husband (which actually happened, only she got taken along with it).
I, for one, like the fallibility the arbiters have. It makes the show interesting. I was actually hoping at the end of episode 2 that it isn't going to be "It's all according to plan." - Decim, and it was not. Decim is actually a character that can and will grow.
@David - Right and wrong is a purely human construct. That does not make it invalid in this case. Judgment, by its very definition, requires a standard or basis. It just so happens that these arbiters use something similar to what is socially accepted for modern society.
The latest episode showed that two people can get reincarnated. The entire game is just a show to bring out the true colors of the deceased, nothing else.