I'm bad at empathy. I've gotten better in recent years, mainly through observation and explicitly linking people's expressions to their later actions or statements. (For example, people who are not smiling or talking a lot are more likely to be upset, if you ask them. This might be obvious to you, but it took me a while to get this.) This was much worse when I was younger, so when thirteen year-old me picked up the library's new copy of Promise of the Witch-King and found within its pages someone else who got scolded for lack of empathy but seemed to be doing perfectly well without it, I was pretty excited. Road of the Patriarch wasn't out yet, so I went backwards, to Servant of the Shard and then all the way back to the Dark Elf Trilogy. I find this worth mentioning mainly because Entreri gets worse at empathy the further back you go.
Consider The Legacy, when he's disguised as Regis and talking about Artemis Entreri to Drizzt. It's fairly obvious that he's monitoring Drizzt's reactions for indication that Drizzt is just as obsessed as he is, and he's having difficulty reading Drizzt's actual emotions. Consider his continual surprise and inability to pick up when Drizzt is truly done with the whole conversation. Part of this could be chalked up to wishful thinking, but at least some could be linked to a difficulty interpreting other people's inner landscapes. (Note that this isn't really a detriment to his line of work. Regardless of how someone feels, they usually only have a few different lines of action they can take. Entreri doesn't need to understand Drizzt's feelings of friendship to predict that the ranger would chase after him to save Regis, for example.) And later in the same book, when he is supposed to getting his fight from Drizzt, it takes him surprisingly long to pick up on the fact that Drizzt just isn't going to fight him without proper motivation.
From reading "The Third Level," it's obvious that Entreri's lack of empathy is from a different source than mine. His is an intentional response to a harsh world where empathy hurts, whereas mine is innate. (Yay Aspergers.) But thirteen year-old me didn't know that, and twenty-three year-old me doesn't care. After all, choosing not to have it still meant that, when he was trying to understand someone's emotions, he had difficulty. Empathy is a skill like any other, and one that he deliberately didn't develop.
Perhaps this is why I felt so betrayed by Road of the Patriarch. Looking back on the series now, Jarlaxle seems a much more fallible character, but I definitely didn't pick up on that when I was younger. Jarlaxle was trying to fix Entreri. But if he was broken, then so was I.
I'm still pretty pissed about that, frankly. Like, I have a long list of things I hate about that book --one of these days I will write a scathing explanation of everything that's wrong with the pacing-- but the implications of Idalia's Flute are high on the list.