Too much starch is cuts back on protein consumption. Onions will give eggs an "odd" flavor, that I've heard works fine if you're making breakfast but not for making a cake. I had a chicken get sick by eating too much of an avocado (she's fine, $80 later...). Too much sugar is not good for them. Raw potato peels might contain solanine (sp?) and make them sick.
I give mine pretty much anything that isn't rotted. I put onion and spud trimming in the compost, same for asparagus stumps. They like the leftovers of what my kids don't eat - partial oatmeals, bits of omelet, butter sandwich or peanut butter sandwich edges. I also give them cooked meat trimmings and gristle, and sometimes let them pick bones clean.