Non-synthetic lens vignetting in terrestrial imaging is not such a bad thing. It helps to draw the eye towards the subject, and can also sometimes assist in giving the image a romantic and/or mysterious look and feel.
Very nice shootin' Frank, especially for your first time at it. Optical vignetting can add a cool effect but if that's not what you're after it can be removed in post process. Both Canon's Photo Professional and Photoshop CS3 and CS4 have lens vignette correction. It takes a little practice to get a feel for the sliders and a good bright monitor but it offers a solution.
I have the classic 5D and have the same issues. Full frame sensors are wonderful but they are a lot of sensor to evenly light. Fortunately the vignetting won't be so obvious in all situations. Shooting against a bright sky will be about as severe as it gets, at least in my experience.
When imaging white subjects in bright light it's a good idea to dial in some exposure compensation. Start with -1/3 and check your histogram to see if your highlights are holding up. It also helps to try and wait for the bird to get more fully illuminated before metering and focusing. This way you'll get a more accurate metering and have a larger area to get a read on. When you meter a bird that is mostly shadowed it's likely the camera will adjust for the shadow and that will result in the highlights getting blown out. I shoot about 80-90% of the time in AV mode using Evaluative metering. For flight I activate the center focus point, it offers the quickest focus response. I mentioned to Warren about shooting Manual or switching to spot meter, but I don't usually go that route unless the birds are backlit and very dark in color. In those situation a fill flash dialed down would be ideal but I don't use flash so I try to get my exposures based on preserving the highlights without underexposing too much. This insures that I can adjust the shadows in post process and not have a noisy mess.
Are you shooting RAW files?
I'm flattered that you were inspired to go out and try some flight work. I can assure you my first attempts were not as successful as yours. Practice is key for birds in flight. All the technical things will get sorted out quick enough but getting the shots by sharpening technique is what brings home the keepers.
I am a bit slow and stupid today
