I've had day old jell-o shots and they were perfectly fine. I couldn't think of any reason the shots would spoil or anything like that, but if you pour them in paper cups those might get soggy after a few days. You can set the jell-o in the freezer for the initial setting period, but after that keep them in the fridge. My favorite recipe: triple sec, vodka, and lime jell-o.
Jello shots? Never heard of it. I must try it out though. ;D
Jello needs at least 4 hours to hard-set, so Jello shots would need that too.
Jello shots last in the fridge for weeks and I mean weeeeeeks. As long there is no dairy and anything that will spoil. I've made fuzzy naval shots with segments of mandarin orange. I found a few in the back of the fridge that fell off the tray. They were at least 3 months old and guess what? They were still delicious!