Does the Calendar Man say or do anything special on certain holidays?
Yes. If you talk to him on the holidays for your region of the game he will have special things to say. The achievement for doing so is the Storyteller achievement. The Sionis Industries calendar next to his cell (also a Riddler puzzle solution) will have the dates circled. After speaking to him and reloading the area, the month will be marked off on the calendar. The first one to come up is Halloween on October 31st.