There are actually a number of signs (if they're still there) along the Wilmington Trail that identify different sections of the trail ... I don't remember them all off the top of my head, but in addition to "The Mudhole", there's "Fir Wave", "Marble Pitch", "Deer Valley" and "Bear Den Corner". I think there may be one or two more.
I think ski patrol and mountain operations use them for purposes of more specifically identifying the location of a problem along the trail.
As for "The Mudhole" name ... I don't know .. . maybe when they cut the trail that area was a big muddy mess?