Remember, Menzel had to go from formal wear to green makeup/hair/costume. I bet they started getting her ready an hour before she had to perform. Then she had to de-green herself and get back into formal wear and makeup. I'm sure that the craziness backstage, and the anxiousness of the moment, had an impact on her performance.
"The Spectacle has, indeed, an emotional attraction of its own, but, of all the parts, it is the least artistic, and connected least with the art of poetry. For the power of Tragedy, we may be sure, is felt even apart from representation and actors. Besides, the production of spectacular effects depends more on the art of the stage machinist than on that of the poet."
--Aristotle