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.
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.
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.
Several MPs including Lord Caversham are shown wearing top hats in Parliament. MPs didn't (and still don't) wear hats during a session of the House, unless they are raising a Point of Order while a vote is in progress.
The Speaker is shown calling MPs to speak by naming their constituency ("The Honourable Member for Witney" etc). British MPs do address each other in this way, but the Speaker calls MPs to speak by naming them personally.
At the reception at the Chiltern's home, Sir Robert is requested to meet the Indian Ambassador. In 1895 India was a British possession and there could not be such an Ambassador who represents only independent states.