Assuming the finish is bare stainless steel without those newfangled fingerprint-resistant coatings that can be damaged by abrasives ... Bar Keepers Friend works nicely. Apply and rub gently in the direction of polish marks with a wet (not dripping) cloth. Rinse a couple times (with a near-dripping cloth) and dry. It works by removing the oxidized surface layer of the SS which then refreshes itself in a few mins.

I have the same problem with my stainless steel dishwasher and everywhere I read, no one had any complaints about this model, so I'm thinking I have a defective one. I called the manufacturer and they wouldn't do anything since they said I waited too long. I looked at various ways to clean and one suggestion is to use baking soda and water. With a soft towel and in a circular motion, rub the paste mixture all over it. When done, apply some water and wipe it down with another soft cloth. I then use a stainless steel polish and cleaner I get from Amazon. I spray all over the front of the dishwasher, and then I will use a paper towel and very gently just wipe off some of the residue. If it doesn't look right, I will then use this spray again and then gently use the paper towel to wipe it again. It's a continuous problem and one I just to have to deal with for now. Mine needed to be done today so I took a picture of it before during and after. In the after picture it looks like has some streaks or something but it's reflecting things from the other wall because in person it is bright and shiny again. I hope this helps...