Does oxygen desaturation on a long-haul flight (13.5 hours) cause any sort of brain damage to a baby? i've read they go as low as 80% and lower.

Unlikely: Couldn't have said it better myself: "if your baby was born at term and is healthy with no evidence of respiratory problems, then it would be safe to fly. If your baby has any problem with his or her breathing eg. An upper respiratory infection, it would be wise to arrange for your gp to see and examine them before you go." - dr. Jo lee of babyworld.

Odd comment: Babies with a normal lung structure will maintain normal oxygen levels on a long flight the same way any adult or older child would. There is no drop in the blood oxygen level during a flight. Pressurized air craft are a safe mode of travel for infants. Someone is providing you with goofy information.