I just searched on google 'can you use old dish water on veggie gardens" and found this website:
http://extension.umass.edu/landscape/fact-sheets/recycling-gray-water-home-gardens
They say that the phosphates aren't the problem, it's the sodium that is in the soap too. Also, the food particles if applied directly to the top soil would cause mold (that's my opinion not on the site). Grease is supposed to be an issue when applying directly to the soil/plants, which is why most gray water systems use some sort of filter to trap grease before applying to anything. This website says that the main reason to avoid using on veggies is just in case any sort of disease causing pathogens are existing in the water and that they don't transfer through to the food. They do say that if you have to use graywater on your veggies to only use it on plants like corn, tomatoes, broccoli, or anything that doesn't grow
underground (like potatoes or carrots) or lettuces. They specifically say not to use it on greens, or anything that could get the water directly on the edible part of the vegetable.
Anyone considering using graywater for gardens who hasn't before
should check it out, it seems to be an informative website.