Well, I don't know of any quirks simply because I have never used another 500 mm lens!
For birds in flight, keep your shutter up. 1/1600 or faster works best for me. Again, I don't know that that is specific to this lens or is true with any lens at that focal length.
The OS works well. This is a photo of the first grizzly I saw last May in Yellowstone. It was cold with scattered snow flurries and the bear was just coming over a hill. This is hand-held at 500 mm with a shutter speed of 1/400. Between the cold and the excitement, the OS saved this photo.
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If you have never used a lens this long, there will be a learning curve. 500 mm is long and any shake will greatly affect the image quality. Practice, practice, practice.
OBSERVE THE BACKGROUND AND FOREGROUND OF THE BEAR. THERE IS BLURRING. I THINK IT IS ALMOST IMPOSSIBLE TO ACHIEVE HIGHER DEPTH OF FIELD WITH SIGMA 15-500 MM LENS.