Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
Very Varied
If you're looking for one perfect word to describe the tone of Dubliners, you're out of luck.
At times, Joyce is best-friend sympathetic towards his characters and their situations, as in "Araby." There's no making fun of this kid; he's serious when the boy says, "My body was like a harp and her words and gestures were like fingers running upon the wires" (Araby.4).
But sympathetic isn't the only tone Joyce has in his toolbox. He often manages some pretty slick layering of one tone on top of another, so that we can hear two different attitudes towards a character at once.
"Clay" is a great example of this technique, which really depends a lot on the kind of third person narration Joyce uses (see above). The narrator exclaims, "But wasn't Maria glad when the women had finished their tea and the cook and the dummy had begun to clear away the tea-things!" On the one hand, the tone that's right there on the surface is one of elation. The narrator's attitude toward the situation is just like Maria's.
But on the other, there's some distance between this exclamation and the narrator's actual attitude. In that little bit of distance, the tone seems to be something like pity, since it's so easy to see that Maria is very simple-minded and, as a result, also so easily taken advantage of.
It's sort of like the narrator parodies Maria, or draws a caricature of her with language. Her exaggerated characteristics become noticeable for a reason, so that the narrator can direct us to see how our view of the character differs from the character's view of herself. Admittedly this is more than a little complicated, but it's just not right to say that Joyce's tone in "Clay" is one of "elation" or of "uncomplicated acceptance." That's Maria's tone, which the narrator uses to magnify his own, more nuanced understanding of her.