So, if there was a problem at some point, it has solved itself now. Anyway, I've now just started Act 2, and whenever I pick up an upgrade, the slot DOES turn white. Although: As far as I can tell, the slots under the characters were not turning white.
Right about when you posted it came to mind that maybe the upgrades were being applied automatically. Thanks so much for your response, and sorry for being so slow about thanking you.