the "P" Looks like a die chip. Or the punch simply had an issue. The "doubling" to me looks like
Machine Doubling, since the "NUM" all are slightly doubled in the same direction - left to right. There is no added hieght thickness, its nearly on the base of the coin, so its probably MD.
If the letters or numbers aren't thicker than normal or obviously doubled at the same height or thickness, then its not a doubled die.
If the letters or numbers aren't close to the same height, or if the orginal numbers or letters are reduced in size, or parts are missing then
Machine Doubling is suspect.
This site offers an education on
Machine Doubling vs.
DDO's. Most are quite obvious.
I suggest you book mark the page(s);
http://www.errorvariety.com/OFD/MD.html This is NGC's variety plus area. Look up the coin here by year. Many have pictures, so click the listing and try to match your coin to the example.
http://www.ngccoin.com/vp-categories.aspxDo a google search of your coin you have a question of, sometimes it will produce a decent article and if you click on the pictures area, it may even show examples.
All it takes is a bit research to figure these out on your own. For coins that are stumping you, I am sure many will help including me.
Circulated coins are usually tougher to determine if there is a significant issue. The toning, grease, oils and other items can get on the coin and distort the view of the coin.