The black spot can be from one or two sources. The first, is a called a stuck or hot pixel. Your camera's sensor has 12.9 million pixels (12.3 million are used for the image). Many times, a hot or stuck pixel is a bright color - red, yellow, green, etc. It can be any color however. Dark or black pixels can also be called dead pixels as they look like they're "off." Regardless of which your camera suffers, it will not respond to light projected on the sensor by the lens. You'll have to have manually edit the pixel in each image, or return to Nikon for sensor replacement. Nikon used to perform a mapping out of the pixel, but it seems that they don't do this any longer. A sensor replacement can cost in the hundreds of dollars.
The second source, is dust on the sensor. A pixel(s) blocked by dust will show up in each picture, but will appear to be more in focus in some images than others - depending on the aperture value of the camera when the exposure was made. A stuck pixel usually has a very definite edge on all images regardless of aperture setting. A simple, careful wet cleaning of the sensor with a product designed specifically for the job
can solve this problem pretty quickly.
Here's a video for wet sensor cleaning from Youtube
There are others here too. I hope this was helpful & good luck!