RuggedCircuits:
... If you try to run an ATmega328P at 16 MHz and 3.3V it probably just will not work (or not work reliably). My calculations say the maximum frequency at 3.3V is 13.3 MHz.
I run an Uno/328 on 3.3V at 16MHz everyday without any troubles. It's not the best solution, but whenever I have to interface with 3.3V sensors, I just run the entire circuit at 3.3V and it works.