There are some little colored dots appearing on the images taken in my Nikon D40?

There are some little colored dots appearing on the images taken in my Nikon D40.

Do you have a sample shot that you could upload somewhere and post it here?

It could be image noise (but i know that you post here quite a lot, so you most definitely are aware about noise) or hot pixels. Hot pixels can be fixed using special post-processing software, as they always occur in the same locations. The pixel at that location is then filled with an average value of its neighboring pixels by that software.

Could be several things. Have you cleaned your lens recently? If you have other lenses do the same dots appear regardless of the lens? Do you change lenses often? If you do, it could be dust on your sensor. If this is the case I'd suggest having a professional clean it.

The worst case, depending on the camera's age and shutter count, could be the sensor is going.
Since you didn't mention the age or shutter count I'm not telling you that it's bad just a thought.

First try the cleaning, compare shots from different lenses, etc.