Character mistake: Stottlemeyer says that the human finger was "still bleeding, freshly severed." But prior to him saying this, when we are shown the finger, there is no bleeding whatsoever and the blood on the severed end had already dried.
Continuity mistake: In the opening sequence, the uniformed cop who finds toddler Tommy holding the severed finger bends down and says, "What've you got there, big guy?" In full shot, the cop is bare-handed. But when we cut to a close-up in the middle of his line, he's suddenly wearing a latex glove.
Answer: The two men are trying to work out a secret deal between them without involving the union, which means the workers' interests aren't being represented and defeats the whole purpose of a union. The mayor would lose labor's support and Cusack's union troubles would just be starting.
Captain Defenestrator