That's strange. Happens to me as well sometimes, usually when I somehow get two or more faces on top of each other. Try deleting the face and if another remains, then keep deleting until the face disappears and then hit a single undo to assure there is only a single face. If there is only one face per cube, then I would definitely do as Mike said and group them before applying the texture to isolate all the geometry. You could also try running the Cleanup 2.0 script from Thom Thom and this does a good job of eliminating any unseen model issues.

Sorry, first video was mangled by youtube down to 1 second... I've uploaded a fixed video! This shows the problem I am having... http://www.youtube.com/watch?v=RAh-U6oZnJ4