If you’ve navigated the minefield of a family feast, the least you can do is make the most of your spoils. Turkey — along with chicken, capon, Cornish game hen, quail, goose, duck and pork — has a higher proportion of unsaturated fats in its fat tissue than beef or lamb. It has nothing to do with how they look in that dress (unsaturated fat is actually better for you than saturated fat), but unsaturated fat does produce off, stale, cardboard-like flavors in meat that’s been stored and reheated.
When unsaturated fatty acids are damaged by surrounding oxygen and the iron from the meat’s own myoglobin proteins, the vaguely-defined “off” flavors occur. This damage happens slowly in the refrigerator and more quickly when the meat is reheated. The meat hasn’t gone bad, it just doesn’t taste as good as it did the night before.
The most obvious solution is not to reheat meat. Cold chicken tastes fresher than warmed-over chicken simply because the fat-damaging reheating step is skipped.
Another solution is to reduce the meat’s contact with oxygen, either by blocking oxygen during storage in air-tight containers or by seasoning the meat with vegetables, herbs or spices that are high in antioxidants. Cranberries are probably nearby, or pomegranates for fancy eaters. Oregano is also high in antioxidants, as are dill, thyme, rosemary and peppermint.
Nothing can be done about the iron content already in the meat, but not storing the food in metal containers will keep the unsaturated fatty acids from having traumatic encounters with added iron.
If the meat must be reheated (which you probably should if it’s already been a couple of days), reheat it gently and maybe cook it in a flavorful sauce. Meat is more tender when cooked over low heat, and this is as true for leftovers as it is for something fresh from the butcher.
FURTHER READING - Give Thanks? Science Supersized Your Turkey Dinner, Wired - Poultry Fat: Versatile and Good for You, from “Fat: An Appreciation of a Misunderstood Ingredient” by Jennifer McLagen. Google Books - Pre-refrigeration instructions for keeping meat and various vegetables: Miscellaneous, from “Jennie June’s American Cookery Book” by Jane Cunningham Croly, Google Books - How Thanksgiving Got Its Turkey, Good