"It means he took the Hippocratic Oath"
"Hippocratic Oath... that's good."
Falcone found it so funny because of Thomas Wayne's hypocrisy in that he's a doctor who essentially got Falcone to kill Elliot (Thomas' intention or not)
Actually makes me wonder if Falcone thought for a split second that Bruce knew, then and there, but he was making a joke out of it. Could explain why he's so jovial with him later despite Bruce seeming openly quite hostile to him at the funeral, essentially waltzing up to him to talk trash.