Maybe Not So Dumb Question ?

Lets say Denver has a deadline to produce millions of cents but their dies are tired, San Francisco has a few extra and sends Denver what they need. Denver punches a D over the S and starts pumping them out.

Good info Conder!

This. And Sap would have a good run as well, I'm sure.

Yes, I met a lovely example while I was in the Navy.

If you mean US coins I would say no. Until 1964 all proof were made in Philadelphia and wouldn't have mintmarks (exception the proof 1942 P proof warnickel). Since 1985 the mintmarks for the proof coins have been in the master die, but the D mintmarks were put into the working dies by hand. After 1990 all the mintmarks were in the master hubs.

So to get a proof coin with the wrong mintmark a Philadelphia or Denver mint obv would have to accidentally get mixed in with the S mint dies and shipped out for polishing and then to San Francisco for use. The dies are inspected several times under magnification and it would be unlikely they would miss the die having the wrong mintmark. There IS a chance the wrong dies would be sent out, that has happened several times. (Most notably the 1998 and 99 CAM proof cents The reverse die on those is a business strike die that was shipped out polished and used in error.) but it is highly unlikely the mintmarked obv's would be shipped out in error.

The closest thing I can think of to what you are suggesting are the 1999 W tenth and quarter oz bullion coins. In those cases a proof obv die was NOT polished and used to strike bullion coins in error.

Since the dies were shipped out for Philadelphia already hardened there wouldn't be a reason for the branch mints to have mintmark punches. They couldn't have punched the marks into the hardened steel dies if they wanted to. There is 19th century correspondence from the branch mints to Philadelphia on several occasions telling them they had received dies that lacked mintmarks and that they were returning them for replacement. (If they had the ability to put mintmarks into the die, why would they be returning them?) If the few cases where we DO have branch mint dies where the mintmark was put in at the branch, they are not punched in they are hand engraved, usually crudely. (1854 Huge O quarter. 1870 S three dollar gold)