This sort of thing could be a law school contracts exam question. Of course, much like when a doctor tells you you're an "interesting case", that shouldn't inspire your confidence all that much.

The STA made an error in placing the Tartan in their registry, as a result of that error, the thread count provided to the mill was incorrect. The mill was asked to produce 20 yards of fabric in X tartan, with a given STA number. They did just that - they were unable to know that the tartan was registered wrong, since they didn't design it. Am I right on the facts here?

So, other than prevailing on the mill to be good chaps about the whole thing, and remake 20 yards of expensive wool tartan fabric (presumably selling the "mistake" as seconds or a nameless fashion tartan), you might well be stuck with it. Which means you'd either have to pay to have another length of fabric made, or wear the erroneous tartan.

I don't see what your options are. The STA is mostly at fault, and regrettably, the registrant is probably also somewhat at fault for not double-checking what the STA registered. You can come prepared with your biggest smile and ask nicely to see if the mill will correct the "mistake", but then they'd be the ones taking the bath on the tartan, and I'm not sure if they're willing to do that. Won't know unless you ask. If your kiltmaker gives them a lot of business, and asks on your behalf, they might be more amenable, but I don't know the specifics of that situation.

Sorry.