Misplaced Dates can be accidental but most are caused by a mint employee using a date digit punch to test the punch on the die. The digit would be punched in an area where the strike would obscure the letter so it wasn't seen on the struck coin, but it didn't always work as planned.
So some coins will show evidence of a MPD, some will show just one digit and some will show all four. MPD's are often found in the denticles below the date, or near the base of the bust, it depends on the coin series.
Here's a 1854 Large Cent with part of the four visible just below the bust. This variety is called a Newcomb-23.