"rugs generally absorb only a very narrow frequency band and can make things worse. Maybe a small throw rug in front of the speakers."
In writing about room acoustics, the problem I always struggle with and try to make you, our readers, aware of is that it is very hard to speak in absolutes when we talk about sound.
In acoustics, that is, once the electrical signal is "transduced" by the speaker into sound waves, the measurement of said characteristics becomes dependant on the enviroment and the device being measured. The same is true in making statements which sound like certainties, but which are, in reality, are only my or someone else's perception of what they heard, over their system, in their room.
The framework for understandstanding what we're trying to convey then, is to understand from whence it is we speak in such foreshortened formats such as this. (Boy did that sound stuffy! Hope it made a little sense.)
To Az's statement above: True. A rug without padding will affect only very high frequencies. A rug with a wool pad behind it will have an effect lower in the frequency range. The measure of how much and what frequencies are absorbed comes down to thickness of the material. Or whether or not you can make that material "appear" thicker to the sound waves by, for instance, spacing it away from the wall which is often done in recording venues. (And obviously, on a floor, that spacing trick is not practical.)
A rug will, however, change the equation of % desired absorptive material in a room (25%) vs. % diffusive material in a room (25%). And the way in which a rug works, by absorbing progressively more waves as the frequencies increase is linear enough that a standard shelving-type of control (a treble control) can suffice in restoring the highs to re-again balance the mids. (In the great majority of cases this is obviously not the problem. The problem is too much hard, reflective surface area.)
"A small throw rug in front of the speakers", unless it is positioned 1/2 way between the listener and the speakers so that the high, axial-bounce frequencies are attenuated will do little except to add to the percentage of absorption added to the room, and the cooresponding reduction of hard surfaces, subtracted.
"For behind the seating postion you want dispersion. Bookshelves, knick knacks, etc can help dispersion and "
The answer to this depends on the relative distance from the listening position to the rear wall, the type of speaker system utilized (monopole, bi-pole, di-pole) and the distance to the front speakers too. If one is very close to the rear wall then absorption is recommended directly behind the listener to attenuate slap echoes which are relatively strong and can cause loss of vocal intelligibility from the front center channel.
It is, however, often recommended that diffusors be used to the left and right sides of the listening position because they can aid greatly in promoting in a more diffusive rear soundstage by scattering 2nd order (tangential) reflections. The ear is quite sensitive to placement directly behing the head because there your two ears are both equidistant. To one side or the other though of that 180 degree location our positional acuity becomes much poorer. This is why diffusors can be so effective in these locations.