A tipster has contacted Joystiq after getting a reply from the Warner Bros. support team about how to handle a missing code. The process is slightly annoying. Fairly standard for a case such as this, but annoying nontheless considering that the buyer has done nothing wrong.
You'll first need to contact customer service, who will ask you to provide the following: a reciept or invoice for the game (although if you bought from Ebay, you're out of luck), a picture of the game box and disks, a picture of the code sheet (both sides…just in case), as well as your email address and PSN ID/gamertag.
If it's anything like when I needed to contact Warner support for issues with my Lego Rock Band code, it took 2 days to get confirmation that he'd recieved my email containing the pictures and another fortnight to get the new code. This was for a game that was 18 months old at that point as well, and I can imagine they've recieved a hell of a lot more emails concerning missing DLC for Batman.
I can see a good deal of first day buyers just biting the bullet and paying for the DLC.