In electronics, one of the early things you learn is that non-linear mixing of two frequencies will yield new frequencies (related by sum and difference values of the original frequencies). That's your basic heterodyning. Linear mixing does not produce these new frequencies. In fact, a measure of the quality of the linearity of a device (such as an audio amplifier) is to input two frequencies and then measure how much (preferably, how little) of the sum and difference frequencies are present.

The ear has a non-linear (logarithmic) response and thus while we think we are hearing pure, dulcent tones, what we are really haring is a distorted caterwalling of noise. Our brains just tell us that it's beautiful music. But, there are times when we do hear "other frequencies". When tuning a guitar and a string is fretted so it produces the same pitch as another string and the two strings are plucked together, if the tuning is off just slightly, you can hear the beat note as a very low frequency variation.

Radio and audio "follow the rules" and we can fairly easiy relate the theory to the observed result.

The eye also has a logarithmic response but, I have to question if the interference patterns we often see are actually related to that. These would be the patterns seen when looking through two screens or fabrics or fence slats or any other objects that have regular, mathematically related spacings of their elements.

The interference patterns seem to be related more to the "shadows" (perhaps a poor term) cast by one layer relative to the other and are observable equally well by our eyes, with their log response and cameras which typically have a linear response (especially film cameras...which is why a photograph and what we saw at the time are quite different).

Are the visual interference patterns actually the result of "hetrodyning", requiring a non-linear device (such as our eyes) to see them or are they a completly different phenomena than say, RF and local oscillator mixing in a radio receiver?

What you're describing are Moire (there's a diacritical over the e which I'm too lazy to figure out how to type) patterns. This is one type of aliasing, the same phEnomenon which causes wheels to appear to spin backwards in movies. It's similar to interference in some respects, but a distinctly different phenomenon which does not require nonlinear mixing.

The eye doesn't see color by detecting the wavelength or frequency the way the ear does its job, it does so by detecting the energy level of the incoming photons. The interference effects we can see, such as the colors in a soap bubble, occur outside the eye and have nothing to do with linearity or the lack thereof in the eye.

The range of frequencies we can see is under one octive, the second harmonic of a bright 660nm red light is 330nm wich is ultravoillet so I don't think so.