I agree the play is brilliant. It is wonderful social satire, a skillfully executed comedy of manners with much verbal wit. I have seen it live, and I thoroughly enjoyed the movie with Reese Witherspoon as Cecily; Colin Ferth as Jack Worthing; Rupart Everett as Algernon, and Judith Dench as Lady Bracknell. This marvelous cast brings the play to life, and my students LOVE it. Seemingly mundane lines in the mouths of skilled actors become quite hilarious.
But perhaps you meant what weaknesses are exposed? That would be a different question entirely. Wilde does satirize the pretenses of the Victorians, their obsession with name and family and diaries. Nothing, not even love, is felt too deeply, or not deeply enough to interfere with eating.
Even though the play is timely, it certainly has timeless features. We all get caught up in trivialities. Watch any episode of "Seinfeld," and you'll see what I mean.
Lmetcalf nailed it in many ways and it was so funny to hear the student response!!
I also agree that the play (as all things Wilde) is perfect. However, let's admit to a couple of miscues that may be detected by the non-fanatic eye.
First, Wilde should not have omitted the deleted scene on Act 2. In this scene, Algernon is pretending to be Earnest when suddenly a creditor comes to the country house of Jack Worthing to charge "Ernest Worthing" with a massive bill for eating and running accounts in restaurants. Since Jack ran that bill himself as Ernest in London but now Algernon is pretending to be Earnest in the country, Jack slammed Algernon with the bill and nearly lets him go to jail. However, by Cecily's intervention he ended up lending "Ernest" the money to pay and Algernon was saved. This scene would have added a LOT of flavor to the whole act, but according to lore, it was removed for time purposes.
Second, the women were represented rather weakly, although it is a comedy. I am sure the likes of Lady this and Lady that whom were always invited to see Oscar's plays were not too pleased being satirized.
Third, it is definitely a piece of its time. The whole deal of "rightful names", and all that other Victorian vocabulary is hard for the modern student to follow unless you are really into Wilde.
Finally, the comedy is not meant to be funny, but real. I saw the play live once, and half the students (the ones with no clue about the story) just didn't get it. They couldn't get the sarcasm of Algernon's words, nor why Gwendolyn and Cecily were so dimwitted. That, however, was their fault, for one should never see a play without at least building some schema first.
I personally think the play is brilliant -- no flaws! But I can report that my students are frustrated by the sheer convience of it all -- that not only do the guys get their girls, but Jack really does have brother, and the final straw -- that Jack's name really is Ernest! They are also bothered by the fact that Jack/Ernest is now going to marry his first cousin.
I would also add that while the wit and humor are clearly present on each page of the play, there is a "time and place"challenge to a modern audience, especially a modern, American audience. Americans don't have the same attitudes about class and some of the other societal issues that are the satirical subject of the play.