I firmly believe that this story is what they invented the face palm for. Because good lordy, it's got stupid writ large all over it.
The following panels come from Untold Legend Of The Batman #1 (1980) by Len Wein, Jim Aparo and John Byrne. The portion we're discussing in a retelling of the story from Batman #47 (1948) by Finger and Kane. (Yes, I know, if it's retelling a comic story that's already been published 30 years earlier, that's hardly an "Untold Legend." Go sue DC). So we're looking at a Bronze Age interpretation of a Golden Age story. Brace yourself...
Batman had never managed to find the crook who murdered his parents. Then, out of the blue, Commissioner Gordon asks his help in nabbing a minor crime ring boss:
So now Batman can finally put a name to the face--Joe Chill.
But despite being The World's Greatest Detective, Batman is unable to find enough evidence to shut down Chill's operation...
Face palm #1: Weeks!! It took Batman weeks, and he couldn't shut down a smuggling operation!! No wonder Gotham is still so rife with criminals.
The desperate move Batman makes?
Face palm #2: OK, this just might be the dumbest move of all time.
I mean, couldn't you have just gone there as Bruce Wayne and given the exact same speech? Then called the police, tell them you recognized the man who killed your parents, and have him arrested?
I guess you get extra shock value out of the big de-masking. But that doesn't jolt Chill into confessing, to either the murder or the smuggling. And since Batman is firmly in his "Batman doesn't kill" era, you've ended your career (and Dick's, too, obviously), because there's no way this information doesn't go public. And maybe you rationalize that once you take care of Chill, there's no need for you to be Batman anymore. Sure. But...this doesn't take care of Chill!!
But wait...you haven't seen the depths of Batman's master plan:
Face palm #3: You let Chill run.
OK. I'm not sure what you expect of him. But you'll be right on top of him, waiting for that mistake...right?
And the big mistake you were hoping he would make?
Face palm #4: You know, Joe, you could have just said, "Batman's after me!" That should have been enough to motivate your guys. I mean these guys are crooks, who work for you, and they can't wouldn't be too happy to have the Caped Crusader busting up their gig. So the oversharing doesn't really help your cause any. In fact:
Get ready for it...
THE BIGGEST FACE PALM IN HISTORY!
The guy tells you he knows who Batman is, and you gun him down without even thinking to ask, "who is he?"?!?!?!?!?!?
Of course, we should notice that despite the fact that Batman was supposedly following him closely enough to catch Chill making his "mistake," Batman still manages to to arrive only after Chill is shot. Read from a more cynical perspective, it's tough not to leap to the conclusion that Batman set Chill up to die, thus getting revenge without getting his own hands dirty, while preserving his secret identity. Well played, sir.
Then again, who could have predicted that EVERYONE involved would be SO stupid?!?
There's no way to tell right now if this is still canon. Between Crisis One and Batman Year Two and Zero Hour and Infinite Crisis, the Joe Chill origin story has been jerked back and forth so often it's gotten shaken baby syndrome. "Joe Chill was the killer, but he later teamed up with Batman to fight the Reaper! No, Chill was never the actual killer after all, and we never found out who it was!! No, no, Chill WAS the killer, but he was caught that very night!!" After Flushpoint? Who knows what the status of this story is?
And don't get me started on the 1956 retcon that revealed that Chill wasn't really a mugger, he was a hit man who had been paid to kill the Waynes by a Mafia boss, Lew Moxon, and Chill deliberately left young Bruce alive so Bruce would tell everyone it was just a mugger, and when Batman found out and captured Moxon the don had amnesia, so he passed lie detector tests about the Wayne murders, so...