I just got a 1973 Kennedy half dollar and both sides are of kennedy's face! There is no reverse on it! Does anyone know about this error and if it is worth anything? I will post a picture later after I'm done searching my dime rolls.
Here is one I found a couple of months ago. I was dumping a bag of halves in a coin counter and this one kept rejecting. I finally took a close look at it and realized there was a seam on the reverse. Imagine my surprise when I saw the England large penny inside.
As to why the two head or two tailed coin can't happen at the mint. The obverse and reverse dies have very specific shapes to the die cylinder. Those shapes will only fit into the corresponding collar on the coin press. This makes it impossible for two obverse or two reverse dies to be positioned opposite each other in the press.
There are occasionally flip over errors when a coin doesn't reject from the press, flips over and then you can get an impression of the reverse on the obverse and vice versa but you will still see the original strike as well.