I think that might be a problem on edible crops, as the chemicals in dishwasher tablets/powders are very strong. It could also have a bad effect on ornamental plants, too. 'Grey' water from baths etc can be used on occasion, certainly, but this water is almost polluted, and I don't think I'd risk it on my garden.

You can buy organic dish washing products that will not affect your plants. Saying this I would still be cautious on my veggies!

We use environmentally friendly washing up liquid and washing machine liquid both based on plant extracts. I'd happily put the water on the ornamentals and, if pushed, would use on veg. too - after all we use soapy water to get rid of aphids!