Man, I was hoping you wouldn’t ask me to list them, because I didn’t want to make myself look too fanboyish by giving a detailed explanation, but here goes:
During the torture session in police headquarters, Lane, the Third Ghost of Batman, says in so many words that Hurt is the Devil. In issue 666, both Lane and Damian demonstrate supernatural powers which they claim to have gotten via deals with Satan. It’s a future story, so we don’t know whether it “really” happened, and we don’t know whether they’re talking about Hurt, but it injects the devil directly into the mix as a suspect. Batman even seems to be leaning that way just before the helicopter crash, when he asks “Did I look the devil in the face, and was that fear I saw in his eyes?”, or words to that effect.
It seems clear to me that Hurt tells the Joker that he’s Satan, and that the Joker buys into it. Apart from the Sympathy with the Devil bit, there’s also the part where Joker splits his tongue with a knife so that it takes on a forked, devilish look; he does this immediately after telling Batman that he knows who Dr. Hurt is. The mere fact that the Joker initially defers to Hurt, even briefly, suggests Hurt is something more than a garden-variety lunatic. When he eventually rejects Hurt’s orders, he does it by telling Hurt “devil is double is deuce, and joker beats deuce.”
Someone in the Club of Heroes makes a reference to a Satanic curse just before telling Robin to go help Batman, implying that they think Batman is facing the Devil. By the end of the issue Hurt has placed a curse on the cape and cowl…a curse which apparently had some oomph behind it, based on Final Crisis #6.
There were also general references to the Devil throughout the run. The image that appears on the Bat-Computer when the trigger phrase takes effect is demonic. Early on, I believe Gordon asks Batman why they chose to fight an evil as old as time, and Batman says “I thought I could take him.” There’s hellish imagery used in the original Club of Heroes arc (the painting on Mayhew’s island). A lot of these “clues” are vague, I’ll admit, but they add together to paint a certain mood.
As for why I didn’t buy Hurt’s claim to be Thomas Wayne, he just didn’t seem very committed to it. He seems to be trying anything and everything in order to rattle Bruce at that point: shooting at him, shouting additional post-hypnotic trigger phrases, and then telling Bruce that he’s Thomas Wayne. When Bruce refuses to buy it, he doesn’t argue the point at all; he asks whether Bruce is really willing to consider the only other alternative, which is that he’s “the hole in things,” and I don’t know what that could possibly mean other than that he’s the Devil.