Until the Supreme Court's 1967 decision in Loving v. Virginia, interracial marriage was illegal in 17 states, including Maryland. In 1962 Baltimore, Seaweed and Penny's relationship would've been illegal.
However, as the movie is set in 1962, and the analysis that led to Mt. Chimborazo being described that way was performed recently, it is extraordinarily unlikely that's what the teacher is referring to. Also, by the measurement that lists Mt. Chimborazo as highest, Everest is not 2nd, but 10th. The reference is almost certainly to K2, which is a point of contention.
The Broadway lyrics are: "Ever since we first saw the sun/It seems Von Tussle girls are always tryin' to please someone/But now we're gonna shake and shimmy it/And have some fun, today!"
In the movie, the rest of the characters sing this version of the line: "Ever since we first saw the sun/a man and woman liked to shake it when the day is done/And so we're going to shake and shimmy it and have some fun today."