Muriatic acid is the colloquial name for hydrochloric acid in a concentration between 15% and 30%. That's pretty strong stuff. Even after diluting 1:1, it is still really strong. Your problem is not only that it has highly corrosive vapors, but it also has chloride ions. Tons and tons of them. These ions are really not good for stainless steel. They errode the passivation layer that protects the steel from corroding. Without that layer, it's just the same as any other steel that will rust upon contact with corrosive substances.

So, yeah, as you just discovered, muriatic acid is pretty much a guaranteed way to make stainless steel rust. If you are lucky, corrosion is just on the outside of your appliance and the rest is unharmed. I don't want to hazard a guess as to how likely this scenario is, but I want to believe this ... and so do you, I bet.

If so, then with enough elbow grease, you can restore the looks of your appliance. In order to avoid further damage, I would first remove the outer stainless steel shell from the appliance. It usually comes off once you start unscrewing things. This way, you can go to town with it without having to worry that you break anything else in the process. But it is up to you whether you want to take this extra step.

I would then use a cleaner such as Barkeeper's Friend to remove the extensive rust spots. This is a little tricky. Barkeeper's Friend consists of abrasive material, a detergent, and importantly of oxalic acid. The latter is quite good at removing rust. But, and that's the big caveat here, it also is a corrosive chemical that can in fact damage stainless steel and leave big black spots on it. So, you want to scrub off all the rust, but then immediately afterwards you want to rinse of any remaining cleaner as soon as possible.

There is a good chance that aggressive scrubbing will mess up the grain of the stainless steel panel. After all, Barkeeper's Friend contains a substantial amount of abrasive feldspar. At this point, your panel probably looks all scuffed up. You'll have to carefully restore the grain. When you do this, absolutely avoid any products containing iron. Steelwool is yet another foolproof way to make stainless steel rust. Instead, you should use a red 3M Scotch Brite 7447 pad. If you have a steady hand, move it in straight lines across the panel until it looks uniform again. At this point, you'll thank me that I recommended removing the shell from the door; and if you can remove any handles and emblems, that would be even better. If you can't manage putting the grain back manually (it does take quite some skill to make it pretty), then instead go for a random pattern. Grab a random-orbit palm sander, attach the Scotch Brite pad, and evenly scuff up the entire panel until it looks completely uniform. This still takes some skill, but is overall much easier and it looks quite nice when done.

Now add up all your hours, multiply by a reasonable hourly rate, and ask yourself why you didn't just buy a new dishwasher. At least with a new one, you know that the electronics won't have been damaged by the fumes from the acid.