Dish wash soaps are designed to remove organic residue and germs from plates, not rinse road grime and dirt from a car. Dish soap might be a little hash to use frequently to wash your car. Once a yea won't hurt anything.
Perhaps I should dispel this myth. I'm an R&D Chemist that designs cleaning chemicals (generally for the Food and Beverage industries, but have also made instrument sanitisers for hospitals, etc). I'm an avid car enthusiast also and have been looking into the car wash topic for some time now. It seems to me that a lot of marketing BS is getting propagated as fact, even on this forum. THIS I'm not criticising at all, as you aren't chemists and have no other way of knowing besides what a marketing team put on their labels. I have, however, gotten annoyed with the marketing BS out there and thought I'd tear some of it down to better enlighten you all.
Dish soaps and car wash products use the same surfactant packages. Commonly, SLES (Sodium Lauryl Ether Sulphate), Dodecylbenzene sulphonic acid (neutralised with Sodium Hydroxide, Triethanolamine or Isopropanolamine). You'll find concentrations will vary, but not by much. There will be other additives that make a slight difference - but a couple of percent difference in the bottle become negligible once you pour a capful into a bucket and dilute it that far.
Am I saying dish soaps and car wash products are exactly the same?
No. They'll use different dyes and fragrances. Potentially some silicone emulsions or waxes for an increased shine. Maybe some optical brighteners too. With regards to the actual surfactants that do the cleaning - they'll be the same. And the salt...
My initial thought on the difference between sink detergents and car wash products was this: I know EVERYONE puts salt into their sink detergents - it bumps at the viscosity and makes it easier to work with (also makes them cheaper too). Car wash products won't use salt. (as it drastically increases corrosion rates)
Sadly, this isn't true. A simple silver nitrate titration confirmed it (but I don't want to go into detail about company names, needless to say that I started with 5 different products from a local auto store and now I've tested over 20 based on the shocking results, even from 'boutique' products). Even with some products that claimed to include "corrosion inhibitors." I hate to say it, but loading up with salt negates any inhibitor you add to the product.
There is no such thing as a 'harsh' surfactant or a 'soft' one (unless we're talking skin-care, but our skin is infinitely more sensitive than the polymeric clear coat on your car). They have slightly different effects but all work on the same principle. "Harsh detergent" is marketing BS. No detergent is going to dissolve your acrylic clear coat (the chemist that sits next to me worked for BASF in their automotive paints division for 10 years, he's now been with us designing industrial rust-proof paints for another 10 - he had a very good laugh when I showed him some of the stuff written online regarding this topic). You know what causes much more damage than a "harsh surfactant" to your clear coat? UV Degradation. Paint laboratories world-wide use a UV chamber to try to destroy their paints (so they can prove how long they last) - what they don't do is soak the paint samples in sink detergent.
In saying all this, I know that there are SOME quality manufacturers out there that don't use salt. A general rule of thumb will be to look for the companies that charge good $ for a product but don't seem to have the fancy packaging to match the price tag. That fancy packaging and labelling costs more than the chemical in the bottle.
If you have any specific questions about surfactants, surface tension, dirt removal, corrosion etc feel free to ask. I'm trying not to turn this into a chemistry lesson (as even I find that boring!) yet I'm happy to go into detail should someone require it.