What evidence from a murder in 1913 could possibly exist?

I know almost nothing about Leo Frank's actions, but I know that when it comes to Jack The Ripper, they've basically identified the man in question due to some original DNA samples. Even poorly preserved DNA samples can be useful (in this case because "jack" literally wasn't even English). The big benefit here is that the original detectives had the man as a prime suspect from the start, so it was easy to basically prove them right.

If any of the original material was preserved in some way, you could get DNA tests to isolate out people, and it's possible that additional documentational information (like alibi's) could have been discovered that wasn't available to the original investigators.

Like I said, I don't know if any of this applies in Leo Frank's case, but it is possible that our modern techniques could identify the culprit if good investigative work was done initially, and any amount of evidence was adequately preserved.