Batman and family didn't think it was wise to check out all personal items that had been handled by the Joker...? Especially things that come in direct contact with skin? Ridiculous.
That struck me as well. The DCU's greatest detective and he makes such a basic mistake as that it seems hard to credit and that element really bugged me about this issue. It just looked so obviously shoehorned into the story by the writer purely to set up the future storyline for Jason. Or are we supposed to believe Bruce is so rattled by the Joker that all his common sense goes out the window.