Without seeing your bird, it's hard to say for certain whether his pinfeathers are coming in normally. Often people who call in to my practice describe pin feather emergence to me in the way you have, only for us to see at the physical exam that the molt is normal.
Assuming there is a problem, any one of a number of conditions could be responsible for a delayed or incomplete molt. Let's start with your bird's age. Twenty-seven is fairly old for a Patagonian conure. Older birds can develop arthritis, which often makes it difficult to preen feathers properly. The good news is there's lots a veterinarian can do to ease the pain of arthritis and enable normal preening. Older birds can also suffer from impaired liver function, which can also affect molting. Again, your veterinarian can diagnose and treat many liver problems if they're caught early enough.
Some conditions such as vitamin A deficiency and other forms of malnutrition can result in keratin buildup. This can enable opportunistic bacterial infections to take hold, which in turn contributes to progressively abnormal pin feather development and waxy clumps something like you describe. Other possible culprits: cardiovascular disease, digestive problems, or any one of a number of chronic infectious diseases. You get the picture. Many of these conditions, on top of being progressively debilitating, can be quite painful. For these reasons, and with the best interest of your bird in mind, I would strongly advise that you have him evaluated as soon as possible.
Brian Speer, DVM, is an internationally renowned specialist in bird medicine, certified through the American Board of Veterinary Practitioners (ABVP) as well as the European College of Avian Medicine and Surgery. He is founder of The Medical Center for Birds in Oakley, Calif., an avian-exclusive practice specializing in the care of companion birds; co-author of The Large Macaws and Birds for Dummies; and past president of the Association of Avian Veterinarians.
Disclaimer: Ask A Vet advice is for informational purposes only and should not be used to diagnose or treat your bird. If your bird seems to be ill, injured or bleeding, please consult your avian veterinarian immediately and make an appointment for a physical examination and diagnostic evaluation.