The question is: how do I get rid of these particular seams? I've found a few tutorials on removing seams in UV mapped textures, but these all seem geared specifically towards matching textures that actually don't show gaps. In this image, you can see the seams near the bottom, appearing white. In the past, I have caused them to be black or grey, by having "render alpha" unchecked.
In my UV map, everything looks reasonably correct: the image is 1024x768px, with each "frame/cube-side" being 256x256px. Some of them match up fine, others seem to leave a few-pixels-wide gap. With the UV map, I have checked to make sure the map isn't picking up any unused areas of the texture. The UV map bounds the image perfectly.
Is it possible that this is a bug in the UV map stuff, causing it to pick up a pixel or two of the unused transparent areas of the image? Or is it something I'm doing wrong.
UPDATE: These lines appear exactly on the same edges as the seams I marked. This makes sense, taken with the fact that it's rendering transparency. Why this happens, I don't know.