The west coast has been using greywater to water gardens and flush the toilet for years because we live in a constant drought. There are some "rules" but the one dealing with dish soap is usually "don't." The don't has to do with grease and chemicals you are pouring into your garden. But if you must, use dish soap not dish detergent. Soap is made from plant oils and animal fats. Detergent is all synthetic and contains a lot of not very plant friendly additives. If you really want to pour dish water on your plants, water the trees (or you can always use it to flush the toilet).
For your small plants, use the water going down the drain before you hop into the shower.