Is it safe to eat a dish made with vinegar if the vinegar lid had black stuff on it

You're going to die horribly from cooking in a rusted pan!

Just kidding! A little iron in your food isn't going to hurt you, and can actually help prevent anemia. To quote On Food and Cooking (pg 790): "Excess iron is readily eliminated from the body, and most people can actually benefit from additional dietary iron."

Now, to back this up further:

You won't get much iron out of the pan unless you cook something acidic in it. Rust is insoluble in water without acid present, and in order to become soluble you have to convert to iron nitrate, sulfate, or chloride, according to the solubility table. Nothing you cook in there is likely to cause the necessary reactions to render it highly soluble.

I found a source quoting specific numbers for iron from cast iron cookware, if you are concerned. The gist is that most cooking in cast iron added from 1 to 5 mg of iron to the food, with the highest numbers coming from acidic foods with tomatoes. Applesauce was the highest, good for about 7 mg.

This level of iron intake is quite safe and healthy. To give you a point of comparison, the FDA suggests iron intake of 8 mg/day for men, and 18 mg/day for women, and 80% of the world may be iron deficient. Iron toxicity occurs at about 45 mg/day. So, as I initially stated, you're perfectly safe cooking in your cast iron, and are probably helping your health rather than hurting it!

The used lid had already somewhat degraded when you put vinegar on the jar. These coated self-sealing lids are used in bottling salsa - obviously :) - jams, pickles, condiments, etc all which vary from mild to medium acidity. They work well for the purpose and for the length of time before the contents are used up.

But they were never meant for long term use and when there's even a minor break (not noticeable) between the rubber seal and the inner white coating, it'll start corroding. The 5% acetic acid will corrode the aluminum and other metals in the lid while the combination of 95% water and oxygen will rust any iron that's present. Even home-canning lids will end up corroded by vinegar. It won't happen with first use as in making pickles but people are cautioned not to reuse the flat lid with rubber seal, and not just because it may not seal.

Commercial vnegar comes in plastic bottles with the recycle code 2 inside a triangle. It's high-density polyethylene (HDPE), completely foodsafe and highly resistant to acid. If you can find a small container of the same plastic (such as a 1 L milk jug), that would be a good choice. You're not worried about looks since you're using the vinegar as a disinfectant. It's perfectly safe and would be even if you did use it for food.

I use vinegar to rinse certain dishes and stainless steel in my kitchen after washing. I find it convenient to fill an empty clear plastic dish detergent bottle with it. (I mention this for a reason.) I'm not worried about leaching of the plastic since it's not for food, but it's better not to put vinegar in it if it's to be used for food. It's a code 1 clear plastic, polyethylene terephthalate (PET), that's used for food and soft drinks. Obviously, people aren't dropping over dead from its use but there's concern that phthalates (which are endocrine-disruptors) leach into the liquid contents, even water, when stored in the plastic for long. Better to be safe.

I don't know if your retainer has any metal parts to it. If it does, I have no idea how resistant it is to acids. Your dentist or denturist would be able to tell you. If you wish, you could use hydrogen peroxide and water, ratio 1:1 to both disinfect and whiten your retainer safely. It's actually a more effective disinfectant than vinegar. You probably could buy it in bulk from the same place you get your vinegar from if you choose.