From "The Winthrop Collection" by American Auction Association - Bowers and Ruddy Galleries, Inc., held on September 19 - 20, 1975:

Especially of interest to error collectors will be lot 1020, a unique 1970-S Washington quarter proof struck over a 1900 Barber quarter, taken from a 1970-S proof set, which realized $3,000.

Apparently there were multiple "pieces de caprice" (to steal a term from Don Taxay) produced in 1970. I suspect that the "midnight shift" employee who struck these intended to sneak them out of the mint, but was unable to do so, and simply dropped them in with the normal proofs. If I recall correctly, this Barber overstrike was discovered by a collector in a set received directly from the Mint and reported it to Coin World. It's also listed in Breen's Encyclopedia p. 370 with a reference to a picture in the Breen Proof book 1977 p. 231.

That U.S. quarter over a Canadian quarter may be an example of what is called ‘Mint sport’ in Dick Johnson’s terrific numismatic encyclopedia. The term refers to an odd coined piece created by mint workers for their amusement. It can be a curiosity of various amounts of oddity and uncertainty. Mint error? Sure it is a mint error. The mint made a big error letting a couple of clowns fool around on the presses. Gotta get back to frisking those guys better. Is it worth $35,000? Not bloody likely. But if it is, I will sell this one for 1/10th that sum.

No, they are not mint errors. Knowing mint technology can determine if it is a true mint error or someone fooling around with the equipment. Such pieces can originate any phase of minting, or involve several steps.

As an example of how easily such pieces can be cranked out, here is a photo of a 1940s U.S quarter serving as the host coin for a 2010 Segovia, Spain commemorative medal. Here in Segovia a hand-hammered coin press is used to allow people to strike their own medals under supervision using a heavy sledge hammer. An insider and I had access to it for an hour or so. It is interesting how the profile of George Washington blends with the details of the small medal of which only three exist.

As a test of annealed coin silver (heat softened with a blow torch), I took a few U.S. quarters in VG-VF condition from the 1940s to the press and we hammered away on them. The result was that the dull finish, clean quarters took on nearly a proof-like sheen from sledge-hammer impact on the dies in places. The U.S. 25 cent pieces struck up quite well during this bit of numismatic testing and tomfoolery.