The problem is explained in detail on this unanswered forum post, with more illustrations: http://forum.unity3d.com/threads/unity-5-pixel-scaling-issue.318553/#post-2067025
The basic problem is, I am building sprites out of layers using sprite sheets for each layer. The sheets are all the same size, and the layers are positioned on top of each other at the exact same coordinates. But when they are drawn in Unity 4.6 and higher, they no longer scale consistently. Pixels now bleed through from the lower layers depending on the screen resolution and camera position.
How it used to look, all layers aligned and scaled properly:
How it looks now, the incorrect pixels are scaled differently on the layer below and showing through (circled):