Teeny tiny colored dots in my photo?

I was looking through some pictures I have taken (with my Nikon D3000). I noticed that there are these little colored dots in several of my photographs (all in the exact same spot in each photo). What are these dots? It seems like it must be something on my lens since there all in the same spot.

Or it could be on the sensor.
Change the lens and see if it is still there.

It COULD be lens dust, but it sounds more like either sensor dust or hot pixels on the sensor. I would call Nikon customer support and ask them how to reset your sensor, if cleaning your lens and sensor doesn't work.

Could be dust on the sensor, or hot pixels * if the spots don't move*. Dirt on your lens will be out-of-focus so it's unlikely to be that causing this affliction. If you have dust on your sensor, it will create dark spots that increase in definition as the aperture is closed.So, shooting at f/22 will cause the sensor dust to show quite easily.

If you are suffering from hot pixels, I'm afraid you are lumbered with that, as the only way you can change that is to replace the sensor. Sensors often have one or two that are hot and even on my Nikon D3 Pro DSLR there are one or two which show up, particularly when using high ISO.

My advice to you is to use the lowest ISO possible in this case. This reduces the amplification of the signal from the sensor, and consequently the hot pixels won't be so noticeable. You can also light your subject well which tends to hide hot pixels in a lighter shot or fix the image in PP.

BTW, all digital cameras suffer from both colour and luminance noise. The amount is directly proportional to the ISO setting of your camera, and indirectly proportional to shot lighting.

If they're always in the same position it sounds like 'popped' pixels in your sensor, it's definitely not the lens, any dust in a lens is way out of focus to the point of being invisible when the lens is focused on any subject, the only effect dust in a lens may have is flare caused by light scatter inside the lens and only then when a bright light source is within the frame.

Is there anything in the manual or the menu that refers to 'pixel mapping'? This will detect any flipped or popped pixels and the camera will ignore them, if it still under guarantee it's a valid reason for returning it.

If they occur in different places it could be Jpeg artifacts, take a shot in RAW and Jpeg and compare the two, if they are present in both then it's as above, if they are only in the Jpegs it's probably just Jpeg artifacts.