"Everyone makes mistakes. But then, people's feelings often get expressed in random ways. You're an arbiter; don't just brush them off."

That's what Nona said. To me, that means "It's okay to make mistakes. However, human emotions are more complex than what they superficially appear. You're an arbiter, don't just ignore them."

She scolded Decim for his lack of depth in analysis.

I agree that Decim takes many things into account. What I can't agree with was that the final act was trivial in nature and that it didn't have significant sway. This is evident in how Decim thought he might have been wrong based on that one interpretation difference.

Had it been otherwise, he'd have acted more like you and said something like "I'd have sent her to the void anyway".

It's pretty evident that the final act sold Decim on the idea that the girl was a complete bitch and the guy deserved a second chance.