The broom effect is achieved with a wire that is attached to the broom. There is a release button on the broom that lets go of the wire. The article that someone mentioned went into a lot more technical detail but that's the basic idea.
On tour obviously the show deck is always laid over the existing stage (for the visual aesthetic as well as for the automated tracks/smoke/book stand). If there is sufficient trap space underneath the stage then a trap door is used but not all theatres have enough or any trap room.
In regards to the quickchange, it is rehearsed to the second. Many quickchanges happen throughout the show that you aren't even aware of until you really think about it. Kristyn in NY did her Shiz change in like 20 seconds and that was with the initial wig change that has since been cut.
Since the complexity of the melting effect using an elevator takes up tons of trap space it was cut for the tour (they probally didn't want to pull another Idina as well). Like I said before a lot of the tour theatres simply don't have the room. The projections were enhanced for the tour but there is still some silhouette work done from behind (with the guards and Elphaba).
After the (numerous) flying accidents in Toronto tech week, the NGD effect was cut from the tour 'for good'. A monkey related accident caused a cut from the Toronto run but was restaged for for later tour cities. So that's why Elphaba runs on for NGD.
The NGD tour entrance (since there wasn't the capability of the downstage trap in every venue) was supposed to be Elphaba making her entrance by flying in. A couple days before the the first preview, during a tech run, Steph Block was suspended by 2 wires, one of which malfunctioned and she was badly hurt by the continuation of the other's movement. This was a computer and equipment error NOT human error.
I'm not as knowledgeable regarding the Broadway melting effect but at the Gershwin, Elphaba steps onto an elevator which lowers her beneath the stage while there is rear projected lighting. So on Broadway there is more 'action' included with the projections and lighting then there is on tour.
The melting isn't a projection, the scream is recorded and the rest is done as a play on lights.
"You never really understand a person until you consider things from his point of view - until you climb into his skin and walk around in it."
To Kill A Mockingbird
wicked geek, you are part right however i got to see a bit behind the curtain in philly and i can tell u that minimally dorothy is completely a projection
"Grease," the fourth revival of the season, is the worst show in the history of theater and represents an unparalleled assault on Western civilization and its values. - Michael Reidel