It's a pre-internet, pre-computer thing. Detective work used to be really hard. Nowadays you just shine a black light at stuff and let the DNA-decoder do the rest.
NOTHING escapes Batman's notice.
Police HQ: Least Safe Place in Gotham City. No wonder there's a Bat-signal on the roof.
Damn. Rocky's got (if you'll pardon the expression) STONES. He walked into Police HQ with a machine gun and burned up the little files cards onto which Gordon makes Bonnie write down invasive trivia on everyone who's ever jaywalked (and ever civil servant, but that's another story).
Then Batman, I kid you not, spends, like, 97 panels on Mr. Wizarding the cards back into readability. While YELLING ABOUT IT.
I think the yelling is just SO GORDON CAN HEAR.
Or to keep Robin, who needs to prop up his head to keep from nodding off, awake.
"KEEP YOUR EYES OPEN! YOU'RE GOING TO LEARN SOMETHING!"
Now we wait and allow the red spray to p'rmeate the chrdzzzzzzZZZZZZZZZZZ.
No, really, there's a page and half of this. Somehow it puts the rise of Stan Lee into context, because as annoying as he was (is), he didn't put you to sleep.
Anyway, several science courses later, they figure out that all the victims were part of the Rocky Grimes gang and that he's out for revenge.
A diamond cutter? A concession stand in a petrified forest? What are the odds?!
Golden Age Jim Gordon may be a fat old sissy, but he is a THOROUGH and RELENTLESS fat old sissy. Once you've gotten your first parking ticket he will keep tabs on every detail of your life for as long as you frickin' live. Nowadays, we'd just use Facebook, where we'd know not only when you started working that concession stand in the petrified forest, but what that paella you ate late night looked like sitting on the plate in front of you.
Meanwhile, Rocky, thinking himself safe, takes the next logical step in his scheme, and has a bullet made out of heliotrope. Yes, really. Revenge is a very involved hobby.
His plan is to show up at the "House of Jewels Exhibit" and shoot Brenner the diamond-cutter. On stage, while Brenner is cutting a famous diamond in front of a huge audience (because watching people cut diamonds is a thing in Gotham). Rather than, oh, waiting until gets home. Well, it is a very Gotham-y setting, making it clear that Gotham SWEATS WEALTH, which is why it's so full of crime. Heck, it's a wonder ordinary citizens don't all turn to crime, given that bushels of jewels spill out onto every corner. We'll see how Rocky's plan works out....
Chile! La alegria ya viene!