This type of mint error is very popular among some pattern collectors. On early pieces, such as the Morgan dollar above or the 2 Peace dollars illustrated below, they are believed by some to be trial pieces used to determine the proper striking pressure or the proper die spacing.
These die trials often show different degrees of striking quality as can be seen in the 2 peace dollar trials above.
The 1877 Quarter and Walking Liberty half die adjustment strikes below show an even weaker strike than the peace dollar above.
Photos courtesy of Michael Byers.