1886-1986 United States Liberty Coin Set Half Dollar Coin Error

It really hard to make out. Can it be seen from all angles? Is it on the capsule?

Looks like something was dripped on it. Did you purchase it from the mint, or aftermarket?

It's difficult for me to discern from your images - they are fine, you did a good job with them - which of the two scenarios I can imagine could have caused the issue actually did so.

Scenario 1: As already mentioned by carlp007, a liquid could have dripped on to the coin and caused the discoloration.

Scenario 2. Something could have dripped on to the proof die at the Mint prior to the coin being struck and damaged the polished finish of the die.

In either example, I would imagine the liquid in question was at least mildly acidic.

Multiple examples of the same issue would point to a die-related issue; a single example points to an event specific to the coin. In the absence of others here reporting the same discoloration, I would side with the view that a liquid dripped on to your coin when its capsule was off and the liquid caused the issue.

In any case, I wouldn't consider it an error by the definition for the term that is typically used for coins. Also, I don't believe it is something for which collectors will pay a premium. In fact, it would likely be the opposite.

The coin on the right looks like it maybe have been opened and handled, compared to the one on the left. Probably a drop of something, like sweat, particularly because of the halo around the spot.