The flying in Mary Poppins is really nothing special to anyone who's seen Peter Pan, or any other show where the actors fly(I haven't see WOE). At the end of the show, during the Spoonful of Sugar Reprise, she flys over the stage and then hovers out over the audience. At that point, she extends the umbrella and begins to rise toward an opening at the top of the theatre. You can't really see the harness unless the one of the lights catches on it (I remember that the stage is mostly dark at that point).
Once she goes through the ceiling, she has to make a dash back down to the stage for curtain call. It's very impressive to someone who's never seen flying before, which I'm guessing a good chunk of Mary Poppins' target audience has never seen.
Still, I think the best flying effect I've seen was the flying during Peter Pan. The audience flight at the end was wonderful.
"You drank a charm to kill John Proctor's wife! You drank a charm to kill Goody Proctor!" - Betty Parris to Abigail Williams in Arthur Miller's The Crucible