It's been proven that too much citrus can lower birds' protein and calcium levels, which may lead to feather picking and softer shells. Moderation is the key here.
Peels, on the other hand, I would discourage due a potential choking hazard. I can't find anything that says they're toxic, though, so chopping them up into bits may be alright.
Supposedly citrus (as well as garlic and onion) is supposed to give the eggs an odd flavor, but I can't find any sources that prove such. A few people swear they can taste it in the eggs... may just be in their heads.
If the birds have enough it adds a bit of a sulfur to the egg I bet. Garlic and Onions naturally contain lots of Sulfur in them especially Garlic. That's why I love Garlic and Garlic powder. You can use that sulfur to help with parasites. Citrus fruits I believe have Sulfate in them which is I think a weaker version of Sulfur. I can believe that it could possible lower the nutrition in the birds if too much. I use my knife and cut the fruit in half so they can actually eat it. My chickens never touch the fruit if it's not cut open. Same with milks though; sometimes if the cow was on fresh alfalfa for a long time it tastes different then a dairy cow that never goes to pasture.