Well, if we assume that we're all listening to redbook CD, we have 44,100 discrete voltage levels per second, and lets say we want to be able to swing from 0V to 12 V in a single sample. To do that we'll need a slew rate of:
12/(1/44100)= 0.5292 V/usec
OPA2111's slew rate=2 V/usec
This means that the OPA2111 should be just fine. Now let's say that we want the output to have settled before the next sample. Within the OPA2111 specs we find the following:
To settle to 0.1%: 6 usec
To settle to 0.01%: 10 usec
A single sample takes about 22.67 usec, which would mean that if the slew rate was infinite the output would always have settled down by the next sample, but due to the fact that the slew rate is not really perfect, it is possible that at high frequencies/output levels the voltage output will not have settled by the time the next sample comes around. What this means in terms of audible effects, I have no idea.
If someone could tell me that would be wonderful. I'm guessing that this means that you may get some high frequency sibilance/distortion if you drive the opamp too hard. At half the volume (6V, which I think is plenty to drive most headphones) none of these problems exist. I guess the conclusion to this long rambling post is that yes, in extreme cases the OPA2111 may be too slow, for most uses it's just fine. I can't wait to hear it.