Wow
That was random. Browsing through a local community theatre group's webpage (http://www.geneseo.edu/~gcp/home.htm), which I decided to look for after seeing a thing about auditions in the Community News circular thingy, I have managed to determine what the name of the movie where strip scrabble was referred to was. The movie is Come Blow Your Horn (1963) with Frank Sinatra as the lead - too many details that seem right when reading the user comments/description for it to be anything else. Here's the imdb link for that: http://www.imdb.com/title/tt0056940/
WOW!
WOW!