They will omit a poisonous gas that is fatal to birds. I have known some people to throw out all their Teflon coated pans after buying a bird. Normal use of these pans is fine, but if they ever get too hot, they can be fatal for your bird. Ceiling fans often injure birds. However if your birds wings are clipped, you do not have to worry about that one.
Many birds love water and when out of their cage love to take baths.
Therefore be careful if you have a sink of very hot dishwater or a tub full of bath water. Also when cooking be careful birds do not get to close to hot pots or hot stoves. Should your bird ever get hurt and is bleeding, there is a product on the market called Quick Stop for birds, available in most pet stores, that helps to stop the bleeding. If you do not have this product on hand, try normal household flour or cornstarch. Both these prove very helpful to stop bleeding.