You are probably thinking of an "error coin". This coin is any coin which does not meet the standards of the US Mint or has a flaw in its design or manufacture.
A mint.
Mint state means a coin in the same condition as it was when released by the mint that struck it.
No US coin bears an "F" mint mark
Mintmarks identify which mint the coin was made at.
A "W" mint mark on a US coin indicates it was struck at the West Point Mint. West Point only strikes commemorative and bullion coins, so you won't find W-mint coins in circulation. The only possible exception might be the special dimes that were minted in 1996 to honor the coin's 50th anniversary. They were sold only to collectors, but it's possible a few may have accidentally been spent.
A mint condition coin is a coin that is in pristine condition, as if it has just been produced at the mint. It will have no signs of wear, scratches, or damage, and the details on the coin will be sharp and well-defined. Mint condition coins are highly valued by collectors due to their rarity and quality.
The letter is known as the mint-mark and tells where the coin was made. A coin having a P mint-mark (or no mint-mark on some coins) was made in Philadelphia, a coin having an S Mint-mark was minted in San Fransisco, a coin with a D mint-mark was minted in Denver.
No. However, there is a George Washington mint coin.
If there isn't a mint mark on a US coin, usually it means that such a coin was minted in Philadelphia.
The coin should have a "S" mint mark on the reverse of the coin, only the San Francisco Mint struck the coins released for circulation and the Philadelphia Mint struck proof only examples. The S mint coins have values starting at $420.00 in the grade of F-12 to more than $1,000.00 in EF-40. If you actually have this coin, show it to a dealer or collector for an accurate assessment.
Mint condition, Mint State, & Uncirculated all mean the same thing. Unused, no wear, as in the same condition as from the Mint when the coin was struck.
The Denver mint is on a coin showing the letter D, this means it was made in Denver, sometimes depending on the coin and year the D mint can be worth some money.