The Cockatoo is likely to have Psittacine beak and feather disease (PBFD). PBFD is highly infectious viral disease. I rescued many PBFD cockatoos in the past as a volunteer. The symptom varies, but in general, they lose feathers (crest feathers, flight feathers, tail feathers etc - depending on individuals and age) and develop overgrown beak. They often look scruffy and have thin layers of feathers (typically shown in face).