This may seem obvious to some, but I wanted to share a couple of ways to keep your birds healthier at feeders which came from the book Why Don't Woodpeckers Get Headaches.
First, "Even though wet, rotting, moldy seed does sound appealing (yeah, right), it really isn't the best for the birds...seeds that are on the ground are mixing in with the droppings from the birds on the feeder above. Feeder birds can pass illnesses on to ground-feeding birds through their droppings. It becomes even more important to clean up under your feeders during wet, cold weather when birds are stressed and more susceptible to disease." The book further suggests to periodically rake (or sweep) under your feeders to prevent diseases.
Secondly, "..the best way to keep [your feeders] clean is to totally empty them every time you go to fill them. Never, ever put fresh seed on the top of old seed or "top off" your feeder...Dump the old seed on the ground for doves and sparrows...or empty the remaining seed into an empty coffee can. Then add your fresh seed and put the old seed on top. Moldy seed is dangerous for birds..."
Lastly, if your feeders are plastic and have accumulated mold, pour a bucket of hot water and add a bit of bleach. Dish soap is fine, too. Take your feeders apart and place all your feeder parts in the tub and let them soak for a while. Then scrub away all the goo and scuzziness and rinse well. Let everything dry in the sun. "Finally, if you still remember how, reassemble your feeders, fill them with fresh seed, and put them back outside for any birds that haven't already filed a complaint with the board of health. "