Hi Tim,
Do you mean accuracy in terms of output amplitude vs input amplitude? If so then not that bothered because I can amplify/attenuate before or after.
If you mean distortion or how "identical" the o/p is to the i/p then I have no idea how to quantify/specify. My background is mostly digital and have been getting into analog only recently. 
Well... okay, what's the signal doing, what's it for?
Being able to adjust amplitude is a big gimme:
- Optos have terrible manufacturing accuracy (CTR 50-200% say)
- It changes over time (mainly the LED fades with use, over some years/decades)
- And of course temperature too
Distortion is where the gain depends on the signal's instantaneous amplitude (or some past history thereof, but that gets even more complicated). We can express distortion in many useful ways: peak, average or RMS error from a best-fit line; distortion of a sine wave, or more complicated wave (THD); mixing products of two or more sine tones (IMD); etc.
Sine distortion is simply that, when a sine wave A sin wt is passed through a nonlinear, one-to-one transfer function f(x), we can substitute it into the Taylor series of the function, f(A sin wt) = f(0) + (A sin wt) f'(0) + (A sin wt)^2 f''(0) / 2 + ..., and reduce the powers of sin^n using trig identities. Some terms will go to DC (e.g., sin^2 x = (1 - cos 2x) / 2 has a constant term 1/2), some will go to the fundamental frequency, others go to harmonics (like the cos 2x term).
If you've not taken calculus, Taylor series isn't going to mean anything to you, but suffice it to say, it is an equivalent form to represent a function (given some constraints, which amplifiers obey so we're good), f'(x) means the derivative of the function (well, also not going to mean much, but if nothing else, it's a basic operation we can apply to functions), and the "..." means it's an infinite series (actually N terms with an error term absorbing the difference; if the error term happens to go to zero as N-->infty, great, it's an exact representation).
And a function is simply the curve corresponding to pairs of input and output values, so, voltages or currents or whatever.
If you were using this for a DC application like setting a power supply's output, you'd most likely be interested in the statistical error approach: how closely does it fit a straight line? Also, what is the zero intercept of that line, do we need to trim that out as well or is it fine as is?
For signals, audio for example, THD is the more useful measure. It's not the easiest to calculate, but to be fair, it's not the easiest to measure the transfer curve anyway; at best you can sample some points on it. Easier to measure it with a signal generator and, say, sound recorder, then let a computer do the hard work (Fourier transform perhaps).

There's also frequency response, how flat it should be over time -- does the A factor vary with w (frequency) as well? Or for a time domain response, say you apply a step, how fast does it settle down within some threshold bound of the target value?
Tim