where Parker's film departs from Wilde's text, it is almost always to flesh out some idea or character trait present in the original. For instance, the film starts with Algernon being chased by debt collectors, who pursue him throughout the action. The play begins in Algernon's Mayfair apartment, but his indebtedness and improvidence are frequently mentioned by the other characters. There is also a scene (cut by Wilde and generally omitted from performances, but available in all variorum texts) in which a solicitor pursues "Ernest" to Jack's country house to collect debts due to the Savoy Hotel. This is reinstated in the film.

The character of Lady Bracknell is also developed along the lines that Wilde suggests. She says that she disapproves of mercenary marriages and adds, revealingly, that when she married Lord Bracknell, she had "no fortune of any kind." Parker plays with this idea by providing a flashback to a scandalous stage career in which she was obviously a much more unsuitable marriage prospect than any of the young people in the film. Her summoning Jack to her London house for interrogation is also entirely characteristic of the persona Wilde created for her, despite not occurring in the play.

The Miramax Films movie adaptation of The Importance of Being Ernest, directed by Oliver Parker, follows Oscar Wilde's original script quite well. Most of Wilde's hilarious dialogue is preserved word for word in the movie. The characterization of the rakish Algernon, the ostensibly more respectable Jack, the fearsome Aunt Augusta, and the naive Cecily is delivered brilliantly by Rupert Everett, Colin Firth, Judi Dench, and Reese Witherspoon, respectively. One can hardly imagine the characters being brought to life more skillfully. The movie starts and ends basically the same way, and the action proceeds without much modification.

The movie version takes advantage of its medium when it can, however, to add a little more to the play than a stage production allows. Thus there are more and briefer scene changes, with readers being treated to a big party scene in London at the beginning of the play where Algy reveals he has Jack's cigarette case, a hot air balloon ride, a tattoo parlor, Gwendolyn's painful car trip, and Dr. Chasuble's inner sanctum. The added subplot of Gwendolyn's tattoo, which is followed up in the closing credits with Jack's corresponding ceremony, provides extra humor. Several cutaway scenes depicting Cecily's romantic fantasies create a visual feast and more hilarity. Greater suspense is added by Miss Prism's flight through the cemetery and hazy memory-like scenes of baby Jack in the capacious handbag. 

The ending of the movie varies slightly from the play. In the play, Jack is the older brother, but in the movie, Algy is older. Aunt Augusta confirms at the end of the movie that Jack's name is indeed John, but she declines to divulge her findings. In the play, it is clear that Jack's given name really is Ernest. The movie ends with a vignette of Bunbury's funeral that is not shown in the play. 

Finally, the serenade Jack and Algy perform for Gwendolyn and Cecily is an unforgettable addition which, when reprised at the end, makes movie viewers keep watching to the very last second. 

Although it might seem impossible to improve upon Oscar Wilde's original play, Oliver Parker succeeds in that unlikely effort with his 2002 movie.

I assume that your question refers to the most recent film adaptation of Oscar Wilde's play: the 2002 film starring Colin Firth as Jack and Rupert Everett as Algernon.  In this case, there are no real significant departures from the text in the film; it is a fairly accurate representation of Wilde's original events and characters.  The three acts do overlap in the movie in ways in which they do not in the play.  For example, in the movie, there are early cuts to Cecily at Jack's country house, though -- in the play -- we do not meet her until Act Two.  So, events from different acts, mostly Acts 1 and 2, are blended together.

Further, the movie does lengthen certain scenes, most likely to make the movie a bit longer than it otherwise might have been.  For example, in the play, Aunt Augusta simply conducts her interrogation of Jack as a marriage prospect for Gwendolyn at Algernon's house; however, in the film, it is turned into a much more formal and frightening (and hilarious) affair.  Aunt Augusta asks Jack to come to her home the next day, and when he arrives, he passes someone we must assume to be another potential suitor of Gwendolyn's looking very harried as he quickly leaves the premises.  Jack is presented, then, to Aunt Augusta and two other very august women who all take notes and look at him judgmentally.  It is even more awkward for him than the original scene in the play.

In general, however, the film does a nice job of capturing the characters and themes and only alters details to make them more accessible to a modern audience or omits them if they would not be helpful to such an audience.  (At one point, Dr. Chasuble makes an obscure reference to an early Christian writer who is unlikely to be understood by a 21st-century layperson audience: it is the comments like these that are sometimes omitted.)