1965 Quarter, No Mint, Cuts On Rim - Error Or Damaged?

to the CCF, BraveAngel21! It looks like someone worked your coin over with a pair of wire cutters. Post-mint damage, not an error.

Yes, post-strike damage--likely intentional.

Diagonal cutters

Also, "No Mintmark" is stupid YouTube clickbait.

In 1965-1967, the law was changed as part of the replacement of silver dimes and higher denominations by clad coins to allow the mint to use any of its facilities without marks. This was because they were replacing a large number of circulating coins in a short period. The law was changed back for 1968.

Thus your coin is normal for 1965, but could have been minted at Denver or San Francisco - there is no way to tell.

More generally, the US Mint did not place mintmarks on coins minted in Philadelphia until 1979 (for the Susan B. Anthony dollar) and 1980 for the nickel and higher denominations. Mintmarks were for the branch mints...

Carson City - CC
Charlotte - C
Dahlonega - D
Denver - D
New Orleans - O
San Francisco - S
West Point - W
Manilla - M

Exceptions

War Nickels - minted 1942-1945 out of 35% silver were marked with a large mintmark over the image of Monticello on the reverse. This would have made it easier to remove them from circulation to recover the silver, but it never occurred.

2017P Lincoln cents - the mark commemorated the 225th anniversary of the founding of the Philadelphia Mint.

There have definitely been cases where the mint has played fast and loose with the law requiring mintmarks.

San Francisco and West Point struck circulating quality cents in the 1980s.

Bullion American Silver Eagles ( ASE): there was a period where a FOIA release seemed to indicate that serial numbers on the straps on monster boxes (500 coin boxes) of ASEs were minted elsewhere. That was retracted, but several of the TPGs had indicated the supposed place of origin on their slab labels. You will see "Emergency Production" or similar for other cases.

Where "no mintmark" is meaningful is on a small number of proof coins minted in San Francisco where the S was left off - an error in the manufacturing of the dies.

@BraveAngel21 PMD

I'll add that these are properly called "No S" proofs. Welcome BraveAngel21. Please don't get duped by all the " no mint mark" nonsense out there.