I would say doing a edge detection, and then seeing how many edges it has.
Colors would not help for a boring picture of a gradient of colors.
However edge detection may match a cartoon where color counts or spread would not!
NOTE: edge deterion will fail for images of bricks or tiles, or say sand. But perhaps these are not classed as boring.
Regular features and effects can be discovered by looking at a images fourier transform. The more complex its foruier transform, the less 'boring' an image is!
Perhaps it is not just edges, but edge distribution that may constitute how 'boring' the image is. A image of a brick wall on the left and a seascape on the right may not be classed as boring.
Another possibility is to look for some object. Say run it through a face detector (free software)
http://face.com/
If the image has a face (or something face like) perhaps it can be classed as not-boring.
It all comes down to -- What do you class as boring?