I never took it that the broom had any importance of particular power. Just an ordinary broom which probably means s much to the WWoW as any other broom. The "Wizard" doesn't really "want" it, keep in mind he's likely just sending the group on a fool's errand, one he doesn't believe they can accomplish since he knows he can't really grant any "wishes" to them.
The thing I never got, and still don't get, is why the ruby slippers were so important. Are we ever told? I mean whatever power they possess obviously didn't do the WWoE any favors considering she got killed by a house falling out of nowhere.
I learned that some trees are alive and take great umbrage at you picking their fruit. In fact, annoy them enough and they'll get so mad at you they'll throw their fruit at you! Wait...
I learned that "Horses of a Different Color" conveniently change colors between shots.