Live theatre productions have different rules than cinema, regarding suspension of disbelief. Most examples of crew or equipment visible, and related imperfect illusions, are not goofs in this genre.
When the medicine has been contaminated, it changes color from white to red, yet Peter doesn't notice. In the conventions of theater, this may be purely for the benefit of the audience, and not visible to the characters on stage.
During "I've Gotta Crow", when Mary Martin bends over and looks between her legs, we can see her tights are ripped down the middle.