The green carnation that Arthur selects for his buttonhole is a subtle homage to Oscar Wilde. Wilde and his "inner circle" of gay friends used to wear green carnations as a way of discreetly displaying their sexuality.
When Mrs. Chevely discover's Gertrude's letter, it is laying atop a yellow book with an Aubrey Beardsley illustration on the cover. This is apparently a copy of The Yellow Book, which was a Victorian magazine of sorts. When Oscar Wilde was arrested on charges of sodomy in 1895, he was carrying what appeared to be The Yellow Book, and because of this association, the publication was ruined.
The play attended by the characters in the movie is Oscar Wilde's "The Importance of Being Earnest." The tall, older man that addresses the audience from the stage at the end of the play represents Wilde who did in reality address the audience when his play first debuted.
When guests are being announced at the political party in the beginning of the movie, the name "Lord Windemere" is called. "Lady Windermere's Fan" is the title of another popular Oscar Wilde play dealing with sullied reputations.
At Lord Goring's Club, a background character says "Come now, Bunbury!" Bunbury is an imaginary sick friend invented by a character in "The Importance of Being Earnest" as an excuse to visit the country. That play is performed in the background in several scenes of the movie.