If you do decide to reference the Arduino ground to one of the mains phase conductors instead of mains earth, here are a few things to watch out for:
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What power supply will you use for the Arduino? Many wall warts have the negative side of the output connected to the mains ground pin - these are obviously unsuitable for your application.
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You must be prepared for the Arduino ground reference to become live at any time, for example if the live and neutral are the wrong way round, or the neutral connection breaks. So the Arduino and everything connected to it must be double insulated from anything the user can touch. Working on such a system is dangerous unless you use an isolating transformer.
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What else will be connected to the Arduino? In particular, is there anything that needs a different ground reference?