In scientific applications instability of output, in any form (amplitude, phase, polarization, frequency, spectral purity, beam cross section, divergence, etc) will impose a noise signal on the actual data signal. Depending on what you're measuring the noise signal may totally swamp the data signal, leaving you no usable at all.
For example: a simple amplitude modulated audio transmission setup is employed, to vary the intensity of the laser beam to match the input audio signal. You have a laser rated for 10% output stability, which when measured varies it's output by 10% up and down in the pattern of a sine wave 1000 times a second, perhaps as a result of voltage ripple across the output of the driver from an insufficient filter stage in the power supply and an overly loose feedback loop in the driver. The result is a loud 1KHz tone in the output.
Pertaining to solid state lasers, where modulation is in the driver:
Additionally, since the laser's output never leaves a certain range, you have to set the drive current bias point on the modulator based on the expected input levels. If your laser peaks at 10mW and your detector is set up to expect between 500uW and 10mW, and you want maximum modulation, you swing the output from 100% to say 5% (because the receiver throws an error when no signal at all is received), for a 95% modulation index. If your peak output keeps changing from instability, you can no longer use a set modulation index or a set level of gain on the receiver, one or both of them have to be adaptive to correct for the varying efficiency of the diode. If you don't correct for this, what happens in an example is at 100mA you would get 10mW at 25C, but at 30C you only get 9mW, your laser diode warms up and you aren't modulating the laser, but the detector thinks you are because the signal dropped to 9mW when the control electronics are saying "full steam ahead!" by supplying the 100mA. Again, noise is imposed on the received signal that shouldn't be there. In this example not only is a false signal received, but a signal of 100% state will NEVER be received, because the diode now only tops off at 9mW instead of 10mW.
Most systems that rely on lasers for communication don't use amplitude modulation to avoid this, but the principle is still valid.
Edit: also in reference to wavelength stability;
Sensors don't read equally for all wavelengths. So a sensor that puts out 1V for 1mW at 520nm may only put out 0.8V for 1mW at 530nm. If your diode's frequency shifts, now the measured output shifts because the sensor is nonlinear. 532nm is relatively stable in terms of frequency, but not in terms of amplitude, or phase (because of thermal transitions in the crystal set).
