Do you have the weight of the 1982-P Lincoln Cent? If 3.11 grams, then it is a Copper Cent and if 2.5 grams, then it is a Copper Plated Zinc Cent. The weight and close up pics might help with the identification of the Error or Damage. I am leaning toward it being a Copper Cent and was either exposed to heat or the Planchet came from improperly prepared Planchet stock.
Can't be sure about the 1972-P Lincoln Cent. Can't tell if there is doubling on Lincoln's Statue's knee and the Chair or a partial Extra Column or it is from a Die Gouge.