Well your other answers have a mix of composting hippies, and semi-correct people. Most garbage disposals will not handle half a citrus fruit. The rind is the problem, however, if you remove the peel, the acidity and fresh scent does help. And the answer is yes, egg shells are good for the disposal. They are thin enough to travel around the blades and big, as well as, thick enough to push out mashed food and smelly bacteria that hide in the crevasses. They also break up easily for the disposer, and go down the drain easily, once they are completely broken up. Don't worry about sewage treatment plants and all that, I'm sure those who mentioned it have never been to one, and I have. Oh, and ice does nothing.
Been to two Garbage Disposal Manufactures, and taken their sales/demo course. Installed/and or replaced more than 20 garbage disposalls, as well as worked at The Home Depot for 8 years.