There are two issues that are probably affecting your results. Your lens is fairly weak in both areas.

• Auto Focus speed and accuracy
• Camera and/or subject movement

The size of a lens' maximum aperture affects the camera's Auto Focus performance. Not only because the AF system has more light to work with when using a lens with a wider aperture, but also because of the physics involved and the use of edge rays by phase detection AF systems. In general, the same camera with a "faster" lens (one with a wider maximum aperture) can focus more quickly and more accurately than with a "slower" lens. Regardless of what aperture is set in camera, focusing is normally done with the lens wide open. The lens is then stopped down just prior to the shutter opening. Performance of the motor driving the lens' focus elements, including the gearing in the lens, also plays a part.

I'm not familiar with the D7000's available options, but most DSLRs in this class allow you to customize how the Continuous Servo AF works. Through the custom menus you can tell it whether to place priority on focus speed (at the expense of accuracy) or accuracy (at the expense of speed). When shooting continuous bursts you can usually tell it to prioritize one way for the initial shot and then shift to another priority for the subsequent frames in the burst.

The rule of thumb for preventing blur due to camera shake is to use a shutter speed no slower than 1/equivalent focal length. In the case of your APS-C D7000, that means 1/1.5 X the focal length used. At the 28mm end you could use a shutter speed as slow as 1/40 sec if you are practicing good camera stabilization techniques when shooting. On the telephoto end you need a shutter speed of 1/300 sec or faster. Image stabilization would help prevent blur due to camera shake, but your lens doesn't have it. In the case of shooting fast moving subjects like your dog, it makes no difference anyway.

To stop motion of fast moving subjects like a dog or athletes in motion you need faster shutter speeds. Shooting football from the sidelines with a 200mm lens requires about 1/500 sec or faster to freeze the motion. The closer the action is to you, the faster the shutter speed that you need. The only way to get faster shutter speeds in the same amount of light is to either raise the ISO or open the aperture wider. If your aperture is already wide open, then higher ISO is the only way to increase the shutter speed. The problem with higher ISO is that the increased noise (and the effects of using aggressive Noise Reduction) will reduce the amount of detail in the image.