A browning agent common to well water besides Iron is Manganese*. This happens to a be a fairly common chemical in well water in the North East at least.
Iron is the most common staining agent and as mentioned a large amount of tomato sauce could cause problems but is not likely.
Jim {BTW: Glisten works well for Iron & Manganese staining and no, I do not work for or own stock in said company}
Because, y’know, it’s…orange. And the rest of it is white. Why do I care if the toilet bowl is orange if it still flushes the poo down? Well, it’s an aesthetic thing.
Anyhow, someone here at work told me about this product called Glisten…why didn’t any of you guys mention THAT?
Well, yes, but my guests will see the inside of my toilet bowl at some time or another. I don’t have them load my dishwasher for me, as a rule. 
Seriously, I know what you’re saying, and I do get it, I just don’t get it. My mother used to obsess over strange hidden bits of housekeeping that would just drive me nuts, and my husband’s the same way. I just worry about the stuff everyone sees or could potentially make people sick. This isn’t either, so I wouldn’t worry about it. YMM,obviously,V
Interesting info.
Yep, it came on suddenly, and the dishwasher is relatively new (less than 6 months old). Also, nothing like this has ever happened to our old dishwasher, even before I installed the filtration system and we’d occasionally get orange water.
It’s also city water, which is chlorinated, fluoridated, and fornicated (not really) 6 ways to midnight. So I don’t expect this sort of thing to be a result of the water.
If tomatoe sauce is the culprit, I would advise Tincture of Time. Either that, or Glisten.
I registered just so I could thank you all for cracking me up. (I needed that!)
Since it’s 7 years down the road now, I wonder if the OP has gotten a new dishwasher. I highly recommend the kind with a stainless steel interior. Mine always looks shiny and new regardless of what I throw at it.
He has. And it has a stainless interior.
But tell us… Did you try Glisten?
Does it glisten?
Step 2, don’t buy a dishwasher with a plastic tub next time. 
Stainless can stain also from some minerals in well water, but yes stainless is better.
I know, we have well water as well - as well as a decent whole-house softener and conditioning unit, which makes a big difference. I have to run a de-lime cycle on the unit a couple of time a year to clear the haze from the metal.
Having had all three, I would avoid a plastic-tub dishwasher at almost any cost. Enamel is heavier and a bit fragile, but even more durable than stainless, and at around the same cost as most plastic units. I got rid of my last plastic-tub unit (a cheapie that came with our last house) right after it stained just like the OP describes.
When Batman is prepared to go down the bottom of the Marianas Trench with his 1920s style Death Ray for, say 20 minutes or so…humming along to DuranDuran’s “RIO”…he uses Glisten in his dishwasher.
If the stain is on the interior of the dishwasher and stays there without transferring to the items being washed, I don’t see a problem here, unless you’re worried about about really snoopy house guests.