From a perceptual standpoint, the main qualities desired of a good late-reverberation impulse response are
A smooth frequency response exhibits no large, isolated gaps or boosts. It is generally provided when the mode density is sufficiently large in the frequency domain, with the modes being spread out uniformly, as opposed to piling up in the same place or separated to form gaps. On the other hand, the modes should not be too regularly spaced, since this can produce audible periodicity in the time-domain impulse response.
An interesting experiment by Moorer  was to try exponentially decaying white noise as a late reverberation impulse response. This signal satisfies both smoothness criteria (time domain and frequency domain), and it sounds quite natural. However, since natural reverberation decays faster at high frequencies, it is better to say that the ideal late reverberation impulse response is exponentially decaying ``colored'' noise, with the high-frequency energy decaying faster than the low-frequency energy.
Schroeder's rule of thumb for echo density in the late reverb is 1000 echoes per second or more [420,421]. However, for impulsive sounds, 10,000 echoes per second or more may be necessary for a smooth response [218,154].