I often come across elements of color which look very natural and realistic despite there being only one solid color (not in a pixel-exact way, but rather in the perceived sense).
When I try to reproduce the effect, for example by filling with one color and not putting any other effects, the color looks bland and boring.
Mainly what effects are used to make colors look more natural? I am aware some use subtle radial gradients and noise. Are there others?
Your eye focuses on things as you look around. If you think of your eye as a camera and look at something backlit your eye will adjust for the contrast and as you look between the brightest and darkest areas it will compensate. Also as you look at things the eye will adjust depth of field. In your illustrations try playing with blurring some edges and sharpening others. this creates a natural feel for something as well as help in pushing focus into areas. This may be the technique your are looking for to bring the natural feel to your one color images.