I took some shots recently and I noticed that I'm getting a lot of little black dots in my images.
I cleaned my lens thoroughly with the Nikon camelhair brush and retook the pictures but once again, the dots appear.
I'm shooting with a Nikon D7000 and using a starter lens. I've attached an example (notice the black spots on the chairs, on the ceiling, etc).
Nikons have a reputation of coming from the factory with a little too much oil on the shutter mechanisms. Some of the excess oil eventually finds its way onto the sensor. What you are seeing in your photos is the shadow of the oil (and the dust stuck to it) on your sensor. You will probably have to go through several cycles of cleaning your sensor before the problem will gradually go away. Any type of dust spots on the sensor (actually on the IR filter in front of the sensor) will be darker, sharper, and more noticeable when shooting with narrower apertures than when shooting with wider apertures.
For more on why dust spots are darker and sharper using narrower apertures, see Question About the D600 Dirty Sensor Test - Why Use a High f-Stop? and Why use a small aperture when trying to see sensor dust?
As to how to clean you sensor, please see What is the best way to clean the sensor on a digital SLR?
Looks like really bad dust on the sensor maybe or even a bad sensor. Do the spots stay in the same place? Issues with the lens wouldn't produces such defined issues because light from each pixel comes from multiple parts of the lens. I would suggest trying to clean the sensor or sending it to Nikon to have it cleaned professionally. If that doesn't work, then it is probably bad pixels in the sensor itself, but it is almost certainly dust or dirt.
I don't think it's bad pixels because the dots seems out of focus and not a single pixel that is not working. Here is a link that you can follow to verify if you sensor is really dirty: http://photo.net/equipment/dslr-sensor-cleaning/
If it is dirty you should look for a tecnical. Sensor is very delicate and I wont recommend you to try by yourself.
here is an example of a dirty sensor.
I too had this exact issue on my 7000. I took it to Nikon UK and they cleaned it for me (the sensor) FOC, but made no comment as to what it was. Since then, two years on, I have had to learn to clean it my self, so its worth buying the right stuff to do it with, with a loupe etc. Its not difficult but saves you money.
I understand that it is iol from the shutter and tends to show itself when using CH or CH settings.
That really does look like sensor dust but I've never seen a case where it's so severe. Do you change your lens frequently? My advice would be to always orient your camera so the mount is facing down as you change your lens to lessen the possibility of getting dust and not to change lenses in dusty environments.
The good news is that cleaning the sensor isn't nearly as scary as it sounds, but you do need to take a conservative approach to it. Use an air blower first, check the result, repeat again and only use tools that make contact with the sensor if a combination of an air blower (I really like Giotto's Rocket Air Blaster) and the camera's sensor cleaning mode aren't enough to get it clean.
