Well first of all, automotive paint doesn't have oils in it. It's not alive and doesn't need "feeding" or "moisturizing" like some literature would lead you to believe, so you don't have to worry about stripping out what isn't there.
That said, dishwashing or laundry detergent can be pretty hard on a coat of wax, which is all that is standing between your paint and oxidation. It depends on the particular type and formulation of wax that you're using, but a detergent can either totally remove, or at least weaken it. This is especially true of waxes that are mainly formulated (or totally) with carnauba wax, since waxes are like oils/greases. Some quality polymer sealants (like Klasse, Zaino, probably lots others) are almost unaffected by detergents.
Besides this however, I would not use detergent on a car's finish because, unlike a proper car shampoo, household detergents are not designed to provide any lubrication. This is important when you're washing dust and dirt off of your paint, which is pretty delicate. Some people have also reported instances of staining or discolouration with their car's trim (probably depends on the trim's age and material). The fact that detergents are pretty alkaline doesn't help either.
Is it harmful to do a dish detergent wash once in a while? No. In fact, some people do it as a prep stage before a major detail, but I personally don't have a need for it. Sure it might be a "stronger" soap to use than a car shampoo, but you're better off keeping the car reasonably waxed, which aids cleaning, and using a proper auto shampoo. Even the cheapest stuff you can find is preferable, and a big jug of the stuff for less than $10 can last you for years! Most can mix up a gallon of solution with only 1oz... there's no need to cheap out on this one folks.
