It seems that Blizzard has ironed out the problems that were preventing players from redeeming their loot codes. The 4.0.3a shattering patch temporarily shattered the WoW TCG loot code redemption process for several days, leaving many players unhappy. Well, this seems to be all sorted out now!
As noted in the official thread, it's possible some players may still experience issues when trying to redeem, but these problems seem to be scarce and isolated. If you do happen to experience any roadblocks in the redemption process, please be sure to submit an in-game ticket.