Fist off, soap and water should be SADDLE SOAP and water. Regular soap will strip all the oils out of the leather, even the good ones. As for getting rid of the black spots, you can try a bit of oxalic acid solution applied with a Q-tip but it will likely remove any age patina as well, leaving "clean" spots. Personally, I would clean it well with saddle soap, give it a light taste of neatsfoot oil and follow with a coat of leather balm with atom wax.