Everything I've ever read say leaving the lid on during the boil is very detrimental to your beer. There are volitile compounds that will precipitate out with a boil. If you put the lid on, it catches the steam that is carrying the compounds out, condenses onto the lid, and drips back in.
Dont worry about leaves/dirt/birds falling in, it just adds to the flavor! After all, its all getting boiled, and should fall out during fermentation. I would take a whole bird out, however.
Seriously, a little ambient air in the batch wont hurt it. If lots of crud is flying around, put something up to block the brew, or use the lid and prop it above the top of the kettle at an angle and a tad offset. This way there is less chance of condensation, and whatever does will drip down to the low angle and off onto the ground (which is why you offset the lid).