You should not add plants infested with a pest that might overwinter or plants with disease. Also avoid weeds gone to seed. I often ignore that last one to my regret. If you are using one of those barrel composters so it gets turned a lot the seeds will probably rot but in a pile on the ground even if you turn it a lot (which I don't) the seeds often don't get all put in the middle of the pile.
I've heard to not add predator poop like dog or cat as it might harbor some disease so I don't, but I would not over worry about that as long as it composts really well before use.
Meat and fats can attract rats, raccoons, possums, and other critters. Dogs might enjoy digging in there. I have buried dead chickens and some other animals and animal parts deep in my compost, but normally when I am putting the pile together and I can bury them real deep. Just yesterday I found a tooth in the garden that probably came from my compost.
Wood shavings are different than wood chips. Both will decompose over time but chips take longer. The shavings should not be any kind of problem but you probably need to turn the pile or at least bury them to get them to break down.
I forgot to add if you leave meat or meat products exposed flies will lay eggs in them as they rot. The meat will rotting stink and you will have maggots all over. If you put meat in the compost, bury it deep.
