One can't really make fun of anything as yet undiscovered. For instance that new material they'll come up with in ten years time is no laughing matter. It's serious stuff. But if you're talking about the Bronze Age then we can be a bit more directed. Pretty much anything to do with iron wasn't going to have folk rolling around on the floor of the community roundhouse.
"Hey, you know when you - like - feel listless and drained ..." - a joke about iron-deficiency is on its way but the audience won't be laughing with any of that appreciative it's funny 'cause it's true recognition.
Bronzing out those creases in your animal skins after stone-washing doesn't sound right but it could work. (That washing technology's from the earlier stone-age, so it's ok.) Although steam-pressing will have to wait until the age-of-steam (which seems to me to be in a slightly different category of timespans, like the age-of-kings).
You would never have been able to iron-out bugs in your new wheels (which had been invented by then of course). You'd have to have bronzed them out.
You'd be part of a more weak-willed community since iron determination wouldn't be around for some time yet. Diets would probably have been unthinkable.
You'll still be able to say things like "He's as hard as nails" but, well, that's bronze nails - not quite as tough and intimidating. He'd be a bit of a softy if you ask me.