I just read the review of your lens on Photozone.de and they show your lens is not as sharp on the long end. They show it excellent at the short end, but suggest shooting a f/8 - f/11 when shooting a 300mm. They went on to say that this increases the chances of CA, but that can usually be corrected while post processing. You do want to use your hood when shooting. It not only protects the glass, but also helps reduce the possibility of lens flare.
If you want, you can email me a sample pic and I'll reduce the size and post it for you. Of course, if it doesn't have exif metadata, then it won't offer much insight into your problem. Perhaps you could explain which settings you normally use when shooting birds. Are you setting the AF points or allowing the camera to select your subject? Are you using Aperture or Shutter Priority or one of the automatic program settings? Are you setting ISO high enough that your shutter speed is adequate to capture birds in flight?
Here are a few of my birds in flight pics with the setting I used to capture them. The settings would change dependent upon available light, but it may give you some idea of what settings are required.
Hope they help. BTW, I nearly always shoot in aperture priority mode.
This was shot at sunrise with a Canon 30D and a Sigma 80-400.
1/1000s f/5.6 at 400.0mm iso800 - F/5.6 is wide open for this lens and I needed ISO 800 because of the low light conditions.
This was shot with the same camera and lens, but on a bright day.
1/1600s f/5.6 at 400.0mm iso400
This shot of a turkey vulture was also taken on a bright, sunny day.
I used a Canon 30D and a Canon 100-400 lens for this shot.
This black vulture was shot under similar conditions with the same camera and lens.
1/800s f/5.6 at 400.0mm iso200