I won't worry too much about this. I'm not sure what your dean would do that can help you in this situation. Put yourself in the shoes of the residency programs, why would they judge you for this hiccup? A reasonable program would feel very sorry for you. For faculty who write a lot of letters, most do not write one de novo each time. I don't think anyone would blame them for modifying the content but keep the format of an earlier letter or mixed two letters up. Maybe contact that faculty involved-- first to thank him for writing you a letter in the first place, then ask him to double check and update the letter if needed. Then send the program a short reminder that your letter has been updated due to error that you weren't aware of. Who knows, this might make you stand out, and it's might be a good thing given how many programs have trouble choosing among similarly qualified candidates.