Michael, my gramma always used to use baking soda and lemon juice to clean a burned pot; I'm assuming the vinegar would do the same. It's a nifty little 'science' experiment - try putting some baking soda in a bowl, then add a little lemon juice, and watch it fizz! I'm thinking probably that 'fizz' is what gets in and cleans or loosens.
As for my poor cookie-cutters - I've gotten them as clean as I could - looking them over, some of them did have rust - little brown spots around the 'seams'; while others just had the black spots from the tinned - whatever.
But at least they're clean, and I don't think anything is going to 'stain' the cookies. Maybe next year, i'll ask Santa for a whole new set!