***"Won't you come in?" is a perfectly usual and correct sentence. You would never say "Won't you come into?"****
True enough, BUT....I think "Won't you come in" is correct when the sentence doesn't continue with "the room," whereas "Won't you come into...." is correct when the sentence DOES continue with those other two words. Of course, in that particular case, no one would ever say "Won't you come into the room?" because it would sound ridiculous to specify what's obvious. But, to me, "You came into our home and changed everything" sounds right, whereas "You came in our home and changed everything" certainly does not.
***"When Mabel Comes in the Room" has a double meaning that "When Mabel Comes into the Room" does not, wicked though one of the former's meanings may be.****
Are you joking, or are you seriously suggesting that Jerry Herman had that other meaning in mind and intended the audience to grasp it?????