In addition to the obvious things that you wouldn't want to put in a compost pile such as meat products, I don't put anything that is considered toxic to chickens because when I turn the compost, they love to get in there and help me. And the thing is full of bugs and worms.
So no raw potato, no part of an avocado and no pits from peaches, nectarines or apricots (the inside of the pit has a toxic seed in there and I'm afraid they might get to that if it really dried out and opened).
I also avoid yard trimmings that are toxic to chickens such as tomato plants, Japanese Anemone, Foxglove and thorny things like rose bush trimmings. Don't want the girls to step on thorns and get bumble foot.