The term you are looking for is a "riddler". A set of sloping vibrating trays that the coins ride along after striking. The top tray has holes in it that are just a hair larger than the diameter of the struck coins. Anything the proper size or smaller fals through the holes into the second tray. Anything too large (bonded pairs broadstrikes and most off-centers) stay in the top tray and fall off the end into a reject hopper. The second tray has holes slightly smaller than the struck coins. Anything smaller such as clipped planchets, unstruck, planchets struck fragments, bowties etc. fall through to the third tray. The contents at the end of the second tray move on and the contents of the third go into the reject hopper. Before 2002 the coins would go through one set of riddlers, since then they go through multiple sets which is one reason errors since 2002 are much scarcer. For some reason you seldom see riddlers discussed when the steps in coin production are discussed. (Riddlers are commonly used in farming where they are used to separate weed seeds from grain. Smaller holes, same idea. Grain tends to come in a certain size and the weed seeds are either smaller or larger.) If they do get pasted the riddlers though they will then typically make it into the bags which are pretty much "counted" by weight. Then they aren't found until the bags are rolled by the armored car services etc. There the mistruck pieces are culled out and are supposed to be returned to the mint but are often kept by the employees and sold to error dealers.
Fantastic post. Thank you for explaining that. I have recently been reading up on the minting process and find it facinating. It's also helping me understand how some of these error coins come into being.
@Eric the Red The Nickel looks to be actually Broadstruck It was not attributed correctly The Dime is Off-Center IMHO