He got it twice as bad as Two-Face, but "All-Face" wouldn't be a good name.

The Savage Skull is a barely-remembered Batman foe, but it's more unusual to see Harvey Bullock acting more the villain, in today's book: from 1983, Detective Comics #528, "Requiem for Skulls" Written by Doug Moench, pencils by Gene Colan, inks by Klaus Janson.

Formerly a crooked cop, after having his face burned off Jack Crane became the cop-killer Savage Skull. He was previously believed to have been killed in a fire in Batman #360, but although Commissioner Gordon had declared the case closed, Detective Bullock didn't buy it. That may have been because he had known Crane, or it may have been part of his ongoing job to discredit Gordon, on the orders of Mayor Hamilton Hill. Bullock sends uniforms to sweep the docks, and one is killed when he finds the Skull: Gordon is pissed Bullock got a man killed going in without back-up, but Bullock gets promoted to assistant commissioner. Most of the cops that see Bullock are mildly surprised he's even still on the force...

Bullock remembers an old youth center Crane used to train kids at, and goes to investigate; and after a chat with Batman Gordon goes after him, with Batman going after them; since nobody takes any backup. Skull is there, of course, and Bullock isn't able to talk him down, while Gordon is only able to stop him from killing Bullock before the Skull comes at him. Taking out his knife with a batarang, Batman then steps into the ring with Skull, a Golden Gloves boxing champ, who probably doesn't have any nerve endings left in his face. He puts up about a page and a half worth of fight! Batman is proud of Gordon for saving Bullock, who says he's going to call a press conference "to straighten a few things out," although Bats seems doubtful. Since the next panel, Bullock double-crosses Gordon, taking the credit for the arrest, accusing him of interference, and calling him an incompetent who should be drummed from the force! That was a bit of a surprise. I was thinking this was early in his character, but Bullock had been around since Detective Comics #441.

Also this issue: redheaded Jason Todd, crying at Wayne Manor, visited by a clown. Literally, a clown. Pre-Crisis his origin was very, very much like Dick Grayson's, except Jason's acrobat parents had been killed by Killer Croc. I'm sure this clown would turn out to be a drunk, or a grifter, or something.