Later this past week, I had the chance to do some handheld flight photography with the 1D Mark IV and the 500mm lens.
Due to the location, tide and light at that time of day, shorebirds were the most abundant targets (I was hoping for some raptors but didn't see any).
The 1D Mark IV's auto focus performance was very good. In general, the birds take a fairly predictable path with minimal clutter in the background or foreground to confuse the AF. However, since I was hand holding, keeping the AF point on the bird throughout the entire flight sequence was a challenge.
Regardless, I got several entire sequences of the birds in perfect focus.