There is much use of irony in the play. In examining the characters and events, there is much more than meets the eye.
During Algenon's arguments with Jack over Jack's cigarette case, Algernon reveals much about himself. One such revelation is the depth of his insight into human nature. He asserts that two women cannot become friends before they have quarrelled. Ironically this is how the relationship between Gwendolen and Cecily develops. The apparently 8greeable women quickly gird themselves for serious confrontation over the personality "Ernest" that either claims for her lover.
The double identity of Jack is replicated in Algernon's "Bunburyism". It is ironical that this is used effectively against Jack. As Jack given his country address to Gwendolen Algernon eavesdrops. He takes down the address and promptly asks Lane to prepare him for "Bunburying".
By her own confession, Lady Bracknell has gone into marriage with hardly any wealth. She should not be rating people for their wealth, as she does Jack, before being eligible to marry into her class. For this reason her interview of Jack concerning Jack's worth is ironical.
Advising Jack regarding his parentage, Lady Bracknell finds Jack's being found in a bag at the railway station unsatisfactory, so she asks him to acquire at least one parent. This appears rather impossible. Soon enough, however, Miss Prism comes to the rescue. Upon Lady Bracknell's own insistence, the whole story of Jack's genealogy is made bare and he does acquire adequate parentage in dramatic fashion. Being called Ernest, as it turns out, is really serious business. The flippant naming of an imaginary wayward brother as Ernest by Jack is ironical. In due time he will need to have to acquire that name to solve a critical problem. This is ironical.