This thread is starting to go some silly places. I've taken photography classes, and I've read Understanding Exposure cover to cover. Depth of Field is a pretty basic concept, and I do know how to use it. I understand that a lower f number means a wider aperture, and a wider aperture means a shallower DOF. A shallower DOF means that the near-far range of distances in focus is shorter. It becomes increasingly shorter as the subject approaches the camera. Therefore, a wide aperture shot of an object a few feet from the lens will have a DOF of a few inches, but a wide aperture shot of an object shot at infinity distance may be many, many feet wide.
Additionally, I know how to use my DOF preview button. What I notice is that the DOF preview button will make blurry objects appear in focus, but it will not make focused objects appear blurry. This means that more of a shot may come out clear due to a wide DOF (small aperture) but as I understand it, anything that is already in focus, should come out in focus (barring other factors such as camera shake). Also, at wide open, the DOF preview button does nothing, because it stops down the lens to the aperture, and wide open doesn't need to be stopped down. Well, it literally can't be.
At no point did I state that shutter speed has a relationship with DOF. Others have pointed out that if my camera is set to shutter speed priority mode, and I change the shutter speed, it will automatically adjust the aperture, thus changing the DOF.
If you look at a full crop of the image, it looks blurry or foggy. Camera shake would produce an image that looks streaky. Also, even the shakiest of hands can still produce a clean image at 1/2000 sec shutter speed.
As I reconsider the image, I may have been more like 40' from the geese, so I should have a DOF that is 11 ft wide. Most or all of the geese were within 11 ft of each other, so some or all of them should be in focus.
I also have a shot with the same problem, and the subject is a single kayaker. He should be in focus. And I have a shot of the front of a house. That's a flat plane, so it should be entirely in focus.
I plan to so some test shots. Thank you for the advice.