slew rate and rise time

Once above a certain minimal value, who cares?

Exactly. However one caveat is that you are using a speaker with a "reasonable" impedance curve. Some speakers designs dip down to 2 ohms (not a good thing)- in this case a much higher damping factor than 10 will certainly help.

The Speaker has the last word here. I have heard a speaker alledged to have a 'Q' of .707 and it sounded almost bass thin.

Yes that is how they will be perceived because many speakers are not designed this way. A Q of 0.707 is "critically damped". It means the woofer goes the most quickly to zero after power is removed without any overshoot (no added oscillations or extra bass notes). Some speakers are designed with a higher Q. This allows them to have much more bass response (higher efficiency with a typical hump in the bass response on a freq plot) but the signal continues to oscillate after the power is removed. (It also allows for a smaller box to achieve good bass output) This means transients and decays are not represented properly (timbre will be wrong) but you get a pleasing thick and impressively powerful bass sound (it sells in A/B shop floor scenarios). Sound is two things amplitude and duration - the longer the bass note lasts the louder or more prominent (impressive) it will seem in the mix.

Does a low 'Q' speaker have what I have heard referred to as 'bloom'?

A low Q speaker is over damped. It will be rather inefficient and will require lots of power to drive it. (This type design is extremely rare) The response will go to zero when power is removed and it will not overshoot, however, it will be sluggish compared to "critically damped". Think of a a typical North American storm door and how it closes very slowly - this is overdamped. It will sound even thinner than "critically damped" a very dry and tight punchy sound given the right copious amount of power to control it. It will not sound like "bloom". Bass "bloom" or one note bass would be from a Q of say 0.9 - 1.2 (actually so common that this may be percieved by many as being "correct" sounding bass whereas Q = 0.707 will be perceived as being bass light or wrong sounding bass)

My guess is that the term "damping factor" was at some time in the past appropriated by audio manufacturers for marketing purposes. The term is defined in automatic control system theory where as the product of the damping ratio and the natural undamped frequency. The damping factor is the distance in the left half of the s or plane along the real axis. It is a term specified wholly in terms of mathematics and is completely generic. It's application is in determining the transient response of a system to a step imput and requires that the system first be expressed in terms of a characteristic equation. Factors that are found in a typical electromechanical system include the torque constant, load intertia, amplifier gain, armature resistance, back emf constant etc, acted upon by appropriate factors.

In short, damping factor as it is understood by engineers in all disciplines is not reduced to a simple ratio of two numbers. Since the term has an actual scientifically accepted meaning, my guess is that the term was appropriated to lend scientific status to what someone was trying to sell.

That all being said, knowing the input and output impedances of the components of a home audio system is helpful in choosing which items to connect together in a system, how to connect the items, and how to avoid or address problems.

Wikipedia definition:

In audio system terminology the damping factor gives the ratio of the rated impedance of the loudspeaker to the source impedance. Only the resistive part of the loudspeaker impedance is used. The amplifier output impedance is also assumed to be totally resistive.

For the accepted engineering definition of "damping factor" see for eg. Automatic Control Systems, Kuo; or, Digital Control System Analysis and Design, Phillips and Nagle. Both published by Prentice Hall. The first edition of Phillips and Nagle has a very nice graphical description of how the transient response of a system changes depending on pole location - of course in the z-plan rather than the s-plane seeing as in that instance the analysis is based on on a discrete rather than a continuous analysis (z in that analysis has nothing to do with impedance but comes from the name given for tranforming number sequences to the frequency domain).

Once you review the definition accepted by the engineering community, you will see that damping factor has to do with a system, not merely one component of the system or one set of measurements of a system. The point is that the term, as it has been 'borrowed' is a marketing tool. This is common in the marketing to audiophiles - see the recent thread on the guy who was trying to sell his product to correct for the "doppler effect". The doppler effect has a real scientific definition and by that definition it makes no sense to talk about the doppler effect occurring within an electronic amplifier.

The appropriation of terms in this manner works in marketing like this - from the naive purchasers viewpoint "Oh, the (name the borrowed term) is something I have not considered in my system. It certainly sounds official, and it's "science" so it must be important. Now there is something that I can purchase that will deal with this. If I don't correct for the (name the borrowed term) then my system will not be optimized. I better buy it. Then I will have dealt with another aspect of system degradation." Of course when engineers and scientists debunk the practice, the response shifts to "Oh, I don't know why it works it just does - you can hear it - although sciene and engineering may be able to send man into space they cannot explain the complex world of home audio" or "but these are not simple sine waves - music is complex."

Actually Musicnoise, I think the origin of the term "damping factor" for audio amplifiers has much humbler roots than classical Control Theory.

In these days of direct-coupled amps, it makes sense to specify output impedance, but when virtually all audio amplifiers had multiple output taps . . . I can see where it may have been handy to express this as a single, approximate number for all output impedance configurations.

And differences in the amplifier output impedance can logically be likened to differences in the amount of stuffing inside a speaker box . . . or the compliance in a speaker cone . . . and if we call this "speaker damping", then "damping factor" for an amplifier is actually pretty concise and specific, especially in the world of published consumer electronics specifications. Just a bit anachronistic today.