I was re-re-re-re-re-re-watching Batman and something jumped out at me.
" I was a kid when I killed your parents. I mean, I say 'I made you,' you gotta say 'you made me.' I mean, how childish can you get?"
Everyone's always considered it to be a huge plot hole, or just the Joker talking out of his ass. But on this viewing, it hit me that the Joker DOES know exactly who he's dealing with. The evidence is very subtle, but it's definitely there.
(Apologies if you're on FB; this is going to be a slightly more cohesive version of my post there.)
Start at the scene of the crime. Jack is definitely not drunk or stoned when he kills Thomas and Martha. He's as calm and calculating as ever. He knows what the hell he's doing, in other words. If this is a robbery that went bad, he'll know who he killed the next day when the lead story across all the news will be the murder of the Waynes. However, given that we know he'll rise to become the second-in-command of Gotham under Grissom, and he's dressed quite well, I think it's more likely that (for reasons completely unaddressed in the movie, but possibly tying to that completely awful early draft Burton wrote that was summarized in Wizard ages ago) Jack is the trigger man in a mob hit on the Waynes. Why, we don't know. But that makes it even more likely that he knows exactly who he gunned down. (Why'd he leave Bruce alive? Most likely a witness, who's too young to think, "Dude was wearing some nice duds for a mugger, and didn't actually take anything.")
At this point, the Waynes are probably a non-entity for Jack for ages. He doesn't care that he killed them; they're just two among many. He doesn't follow Bruce in the press, because why would he?
Then Grissom sends Jack to that fateful encounter at Axis Chemicals where he's supposed to be brought in by Jek Porkins. But Gordon and Batman both show up. One bit of the encounter should stand out: Jack is one of the very few people to get a good look at Batman's face, and Batman smiles at him. Batman never smiles. But he does. We're meant to notice it.
So Jack becomes the Joker. No doubt the face of the man responsible for his transformation is burned into his memory.
One man in the photographs Bob takes stands out to the Joker, because he makes a point to ask. It's also the guy who acts as if he wants to stop the spree of violence on the steps of the courthouse. Joker has clearly noticed him, and Bob informs him it's Bruce Wayne. At this point, I don't think he's figured anything out, but he knows this is the son of the couple he killed.
Joker clearly follows newspapers closely, and probably pays a bit more attention to Bruce Wayne. It might be at this point, or it might be a bit later, but, chances are, he recognizes in one photo the sly grin of the Batman.
Batman clearly takes an interest in Vicki Vale, rescuing her at the museum. At this encounter, Joker, who is batshit insane but still clearly intelligent, comments aloud about Batman's "wonderful toys." He no doubt recognizes the expense required. And, soon after, he'll know that Batman figured out his chemical concoctions in personal care items, and has access to some pretty damned advanced chemical equipment. He'll no doubt know that Bruce Wayne, as head of Wayne Enterprises, would fill both requirements.
Joker confronts Vicki at her apartment a bit later. Here's where, if he hasn't already, he connects the dots. Bruce Wayne is there. He now knows that both Bruce and Batman have taken an interest in Vicki. Bruce confronts Joker, telling him that he knows that he's really Jack Napier, then makes a kind of half-assed attempt to fight him. Joker shoots him and leaves. Clearly, Bruce was trying to distract him away from Vicki. Perhaps it worked. More likely, Joker is smart enough to figure out right there that Bruce Wayne is Batman, or at least he gets confirmation. Either way, he'll be checking the news the next day for news of Bruce's death and, when it doesn't come, he'll know that he prepared himself to get shot.
Why doesn't Joker make a big deal about this? Simple. He doesn't need to. Perhaps his goading Batman to take off the mask on TV is, in part, because he knows Bruce can't do that. But, as completely insane as he is, this version of Joker remains in control. He won't do anything with this knowledge until it benefits him...
...like when Batman is beating the shit out of him on top of a church and confirms his suspicions.
*--For behavior unbecoming anyone, perpetrated in real time over an extended--AH, FUCK IT! MORE MALIBU, BITCHES!!