1981 Dime Error, Double Die, Mint Error?

Sorry. what you are seeing is Die Deterioration and slight Machine Doubling on the edges. If it were a doubled die, then there would be an enlargement of the devices. Not seeing that The die was in the VLDS die state when your coin was struck. The heavy die flow is the first clue of this on the fields.
Attributed DDR dies: None listed
Wexler's site show no known doubled dies for this year.
Variety doesn't list any either.
Not a doubled die. Just a tired die with Machine Doubling after the strike. Spendable.

Yep. It's heavy Die Deterioration, caused by a worn die issue, and Machine Doubling. http://www.error-ref.com/machine-doubling/

I am curious about this 1981 P Roosevelt that I have. Is this a double strike of the reverse on the obverse as a result of Feeder Finger Damage? If so what kind of value do they possess. Thank you kindly.

Even though the reverse of the coin is stamped on the obverse?

On a true double struck coin the letters would not be in reverse, but look like part of a regular strike.

It shows all the hallmarks of being a victim of someone's attempts to make it look like an error coin. When the results were not what they wanted, what to do with it? Spend it. You found it. Now it's here. Spend it and the next finder will probably do the same thing. Or take it to the bank and have them send it back to the mint for canceling. And stop the from happening again and again....