Don't think the problem is intonation; I recently checked that. I think it's the beat frequency between the two notes.
Very interesting. I understand the concept of equal tempered, but didn't realize it also plays into what happens when you play two notes simultaneously.
There are two things at play here and it might be worthwhile to clearly distinguish them:
1) The beats that you get from playing an interval, i.e. two signals with two different fundamental frequencies.
These will always produce a beat frequency at the difference between the original frequencies (f_beat = |f_2-f_1|). This happens regardless of intonation.
2) If intonation is off, then you can have an additional effect: The overtone spectra of both fretted notes can contain the "same note". If any two of these frequencies lie very close to, but not exactly on the frequencies produced by the spectrum of the other then you'll get a beat with a very low frequency, perhaps less than a Hertz. This will result in a perceptible warbling of the intensity.
E.g. You are trying to play a fretted A2 at 110.0 Hz and fretted E3 at 164.8 Hz (tempered). Now ideally (neglecting all kinds of anharmonicities, such as string stiffness, pickup response, finger pressure or anything else that will come to bear in a real situation) the next notes in the overtone spectrum of the A2 are A3, and E4 at 330 Hz, which is also in the overtone spectrum of the fretted E3. But since the fretted E3 was at the tempered 164.8 instead of the harmonic 165.0 Hz its overtone E4 is at 328.6 Hz (1.4 Hz flat), This now gives a beat frequency of 1.4 Hz between these two (strong) overtones, and can lead to a perceptible warbling at 1.4 Hz.
Poor intonation will have a similar effect of shifting two frequencies that "should ideally be the same" such that the beats in the 0.5-3 Hz range become noticeable.
This will happen only on strong components of the overtone spectrum, though, and the prevailing anharmonicities will prevent us from hearing strong beats of that nature in most situations (Or rather, there will be so many of them that again we hear an average volume instead of any kind of beat). Lucky for us, otherwise we'd have a real hard time setting up and playing any fretted stringed instrument.
Also a little caveat, this is just one aspect of what can go on here. I just wanted to clarify that we are talking about two slightly different aspects of beats here.
