Hello, P.J., and welcome to the Grammar Exchange!
“A dress fitting” instead of “a dress fit.”
"fit" does not work as a noun to mean what "fitting" denotes (the act of trying clothes on to check whether they fit).
“A drinking problem” instead of a “drink problem”.
"drinking" refers to the action of drinking, while "drink" refers to one particular drink or act of drinking. Just as we speak about "eating disorders" (NOT "food/meal disorders"), we speak about "drinking problem."
“Dance floor” instead of “dancing floor”.
is perhaps the hardest to explain and, therefore, the most idiomatic. I think it has to do with the economy of the language. If "dance" can mean not only a single act but the activity of dancing, why use "dancing" if "dance" is shorter?