What determines the width of the cone in the Maps app? I have noticed that the "direction cone" in the Maps app sometimes changes its acuteness: sometimes it will get wider or narrower. The cone seems to represent some sort of accuracy/confidence. I'm particularly interested in what factors (environmental?) alter it.

What causes this? (or am I just imagining that it changes at all?)
I believe it's related to the accuracy of the compass.  In my experience, the compass is quite inaccurate and maps do not align perfectly with real life, but usually the actual alignment is somewhere in the cone (I say usually because sometimes they're so inaccurate that it's outside even that, especially when I'm inside a big metal car).  This is similar to the blue circle around the dot that represents uncertainty in your location.

It probably changes its acuteness because the compass becomes more and less accurate over time.  The angle of the device may have something to do with this (based on the built-in compass app and personal experience, the compass seems to be more accurate when the device is laid down flat).