What's the best way to create a subtle, barely noticeable texture?
Those textures seem random and very evenly distributed.
The basic technique is to create a background color or gradient, add a 50% Grey layer above it with its blend mode set to "Overlay" and add some noise to that layer using whatever method your program provides. In Photoshop it's a filter, and I seem to recall it's much the same in the gimp. Adjust the amount of noise (which should be monochromatic) and opacity to suit.