At one point during the "Tom Dick and Harry" number, you can clearly see Bobby Van trip and right himself as if waiting for the director to yell "cut". This occurs almost halfway through the number, and to the right of the screen.
During the "Where Is The Life That Late I Led" number Howard Keel leaves the stage and walks out on a long runway that extends into the audience. This runway is not visible before or after the number though there are several shots from the stage into the audience.
At the time he wrote this musical, far from being a healthy man, Cole Porter (played by Ron Randell in this movie) was a wheelchair-bound cripple who needed constant medical care. His legs had been crushed in a riding accident when a horse fell on him.