Here's a short list of the five things I think have to be right for an image to be successful.
The image has to be sharp. If the subject is sharp and the background is blurred, that's okay, but sharpness really can't be fixed in post-processing, so it needs to be right in-camera when the image is created. There are several ways to ensure you get a sharp image; check the shutter speed, use fill flash, use the professional newspaper photographer grip, use a tripod, with a big lens press down on the lens with your left hand to dampen vibrations, etc. For bird photographers, if the eye is sharp, then the rest of the bird can be out of focus. People connect with the eye! On the flip side, if the image is supposed to be blurry, it needs to be blurry enough, so the blur is obviously intentional.
The quality of light and the direction of light make a huge difference between a successful image and one that's just so-so. The quality of light means shoot at dawn or sunset when the sun angle in the sky is low. This enhances the yellow or golden tones in the light and thus makes the image warmer. For the angle of light ask yourself, where is the light coming from. Is it in front of you, sideways to you or behind you. The basic formula for bird photography is the light should come from behind you. Front -lighting works best for bird photography, but Backlighting makes great silhouettes, and Side-lighting which works great for human portraits doesn't seem to works as well for birds but can work if the light isn't too harsh. If you shoot before the sun is on the subject, like the Peregrine Falcon below, you might need to adjust the White Balance of the image, shooting in Auto White Balance will work most of the time, though.
BORDERS, EDGES & BACKGROUNDS
When you're looking in the viewfinder, look at the background. Is there a branch, light pole, building, Eiffel Tower or anything else coming out of the subjects head? Does the horizon cut the subject into two pieces or is it at the neck and make it look like the head is getting cut off? Then as you look through the viewfinder, take a quick glance around the edges of the viewfinder to see if there is something protruding into the frame that shouldn't. A branch, building, another bird etc.
Why is Exposure fourth? Well, to a degree (within a few stops of light) you can fix Exposure in post processing. But, start by reviewing your Histogram and exposing the image to the right when you're shooting. If you can get even some data into the far right sections of the Histogram the image will be close to an accurate exposure. The Histograms in the Canon cameras I use had five sections to the Histogram. I always try to expose the image so some data reaches halfway into the fifth section. It's very easy then to make any adjustments with the Blacks, Whites, Shadow and Highlights Sliders in LightRoom to finish the image and get an accurate exposure.
Try to create the composition of the image in-camera while you're shooting. Yes, you can always crop to fine-tune the composition later in post-processing but the closer the image is to the final composition in-camera the more pixels you'll save for later use (like printing), or the less time you'll need to process the image. The biggest thing to avoid is the DSLR classic image of a centered subject. By using the Rule of Thirds, or placing small subjects in one of the corners the image will be better. That said, sometimes dead center is where you want or need the subject and the horizon or the bird can be centered horizontally or vertically and the image still works. The Rule of Thirds is really, "The Suggested Default of Thirds" encase you can't decide what else to do with the composition. It doesn't hurt to explore compositional ideas in-camera while you're in the field!
I hope this helps you create better images.
Enjoy! Thanks Tim