I don't have any actual
experience yet with any o fthis, just some research and general knowledge.
The thoughts that come to mind for me are (a) what do you plan to use for feeding your plants in your hydroponic system? (b) what inputs are going into your grey water (soap, detergent, baking soda, vinegar...? )? (c) how do those chemicals interact with one another and what effect will that interaction have on the plants?
For example, you might not want a hydroponic fertilizer with much phosphate in it if your grey water is carrying a load of phosphate from some detergent. There could be some chemical combinations that would actually be reactive and make some portion of the fertilizer ineffective - possibly even toxic.
So, it seems to me, the very first thing is to figure out all your inputs into the system and determine how well they will play with one another.
Other than that, I don't see what would really be different from a hydroponic system running fresh water versus one running grey water.