Will a simple RC filter work with my mechanical rotary encoder, or do I need a Schmitt trigger?
Having just chased a problem using a software based debounce for several days, what I'll add is that for the encoders I was using (green no-name Chinese ones), if you put 10mA though the contacts then the signal is a LOT better.   So change the 10k to 470 Ohms.  

Or if using 3.3V use 330 Ohms.  Solved all my problems.