Ah ha! Thanks, seachnasaigh, it's something in the Render Settings Preview tab. I now have textures showing on the construct like normal instead of the washed out white void that it was before. I'll have to play around with it and see what it actually is that's doing it :D

-edit-

It was the 'Enable hardware shading' option in the Preview tab that did it. It's odd because one would think that wouldn't affect textures, but oh well, as long as it's working properly, that's all I care about.