Like a sense of humor, but only applies to the art of perceiving things as dirty that were perfectly innocent. Someone with a sense of smut might also be said to have a dirty mind.
Everyone else took her comment about "working long and hard all night" at face value, but I couldn't help but laugh to myself. I guess I've just got a better sense of smut than all of my coworkers.
av ZebCanCook 3 november 2008