How does altitude affect sound? So I know that altitude affects the speed of sound because of temperature differentials in the atmosphere, but I am curious what else affects how we hear planes overhead?

When a plane flies overhead, you dont hear a very constant filter at all frequency bands. It seems that lower frequencies are more consistent, where high frequencies seems to fade in and out, sounding much like a low pass filter. 

Is this the product of the temperature differentials between you and the plane changing as the plane moves, or are there other factors? Does moving air affect the sound in any way?
The answer to your question has a lot to do with how waves generated by a moving object propagate. You can see a full explanation here but the short answer is the Doppler Effect which causes pitch to change as the object moves buy you. 

Here is a nice explanation

Edit:

My knowledge is a bit rusty but basically you are talking about a mechanical wave propagating through a fluid (the atmosphere) which will absorb some of the energy (eventually all of it). I would also thing that as the speed of sound changes the frequency of the wave would change much like the changes light has when it crosses different mediums.