He was as stubborn a Mick as ever stumbled out of the Northeast parishes to take a patrolman's shield.
Mick is a derogatory word for Irish people. The Northeastern Baltimore neighborhoods are made up mostly Irish ancestors. The Irish are also stereotyped as being very stubborn, yet McNulty is more stubborn then the rest.
To help improve the meaning of these lyrics, visit "McNulty's Eulogy" by The Wire (Ft. David Simon) and leave a comment on the lyrics box