One thing I'm working on is Background Subtraction. What this does is basically takes a picture of a frame and compares it with any new frame.

If you take a picture (with a webcam...you'll need a live feed) of the calender full and complete, then have people rip off a day on it, you can determine the exact pixels for each day and have the computer/programming/arduino respond accordingly.

There is a sample sketch of background subtraction in Processing.

File/Example/Libraries/Video(Capture)/Background Subtraction.

Hope this helps,
~TSG

Or if you use a camera you could also print a fiducials tag on every page and use reacTIVision.
http://reactable.iua.upf.edu/?software
The only problem there is that your camera has to be quite near the calendar.
Maybe you could use some kind of telephoto lens?

I guess that propably your best bet might be not to look for a single, monolithic solution but a combination of several approaches:

Somebody will need to bring their hands near the calendar (=> proximity sensor, maybe capacitative), apply force to it when tearing off a page (maybe best measured where the calendar is fixed to e. g. the wall), and within a certain timeframe after those two events the visible surface will have significantly changed (=> cam).

Just doing background subtraction might fail due to changing lighting conditions (e. g. night/day) and you need to take into account people passing by or standing in front of the calendar. This might be partly addressed by chosing IR lighting and vision, located as near as possible to the object of desire.

In any case you would have to rule out a whole lot of environmental distractions, at least if you are not dealing with a clean laboratory situation. Nonetheless, I would suggest to iterate over the whole thing several times, trying the most simple approach and see for real where troubles arise (which in turn may as well hint at pragmatic solutions) instead of addressing all possible circumstances beforehand. Good luck!