It's been awhile since I read The Long Halloween, but what are some hints that Gilda might be absolutely delusional?
This is coming from something I read online, but one of the major problems that some readers have with Gilda being Holiday is that it would have been very difficult for her to sneak out of the hospital and kill the Irish Gang on Thanksgiving. Shooting Johnny Viti is more believable, as it's a quick, painless death; even the murder of Milos, Falcone's bodyguard, would be relatively simple to pull off. But the hit on the Irish is a lot more complicated: it's five armed guys in a private hotel room, and Gilda was pretty badly injured by the bomb explosion on Halloween; note that on Christmas, she's still in a wheelchair. It wouldn't be completely impossible, but it certainly wouldn't be easy, either.
I always assumed that all three suspects committed at least some of the killings. One of them started the pattern, and the others followed it for their own killings.
A lot of the evidence points to Alberto, working under orders from his father, with Gilda and Harvey as viable, but still red herrings. As stated above, Gilda is at one point too injured to do one of the killings. Harvey committing the murders would detract from him finally snapping and becoming Two-Face, and getting his Ironic Echo about "couldn't have happened to a nicer guy." This will be debated for sure, but much of the evidence points to Alberto, who early on shows an interest in the family business, is dismissed by his dad so as to not be seen as a threat. The first half of the killings are all members of the Falcone crime family who failed The Roman in some way, by either selling him out or being inept. In the second half, it becomes the family's enemies, such as Maroni. The first killings serve two purposes: Clear house, and also destroy any suspicion that Falcone is secretly behind it all. Of course, the plan falls apart as the supervillains gain more power. Since the series uses so many Godfather allusions, Alberto is basically Michael (seen as out of the game, but the weapon striking at the family's enemies) hiding under the mask of Fredo's ineptitude.
Also, if Alberto wasn't either committing most of the murders or planning on committing more at the time of his "attack," then he would have no reason to fake his own death or go on to murder his coroner.
There is a Wordof God that stated: There were three killers total, Gilda was the first killer till she was injured, then Harvey picked up where she left off, her dialog stated she believed he knew she was the killer but never confirmed. Then Alberto did the remaining murders but claimed credit for all of them
How the hell could Calendar Man have known who the Holiday Killer is when he's spent the entire story arc locked up in Arkham? What exactly has he seen and/or heard to even know about Alberto or Gilda Dent, much less finger them as the killer(s)?
Some online reviews of the story have pointed out that Calendar Man's dialogue covers all possibilities. By alternating between "he" and "her" and mostly asking open-ended questions, he ensures that something he says will seem to be right in retrospect. Notably, nothing he says seems to help Batman solve the mystery in any meaningful way.