OK, so "comedy" covers the "light" description of the tone (see "Genre" for more). But how can an author take a simultaneously "satirical" and "sympathetic" view of the story? It's in the presentation of the characters. Wilde paints sympathetic portraits of the main characters, taking pains to describe the reasoning behind their actions. Even Mrs. Cheveley gets somewhat of a pass for growing up poor.
But Wilde also pokes fun at characters, in their own dialogue or in dialogue about them. Satire is all about exaggerating people's flaws to comic effect. Lord Goring is the narcissistic result of the "Boodle's Club" – a gentleman's club in London (1.114). Mrs. Cheveley "really has considerable attractions left," even though, according to Victorian standards, her expiration date is coming up (or past) (3.245). Lady Chiltern is the winner of the "good conduct prize" (1.66). Nobody is safe from Wilde's lampoon.