People who are trying to update the PS3 with the new DLC released yesterday (packs 1 and 2) should follow the steps below. Here's the information from FarSight:

We understand that some people are having issues with the latest update on PS3 of the Pinball Arcade. Please follow these steps:
1. Re-download the "Pinball Arcade Demo" and the "Pinball Arcade Full Game Unlock" from PSN Games. You shouldn?t have to delete the old version of the game.

2. Install the "Pinball Arcade Demo". When you open the game the trial versions of the new tables should be in the menu.

3. Make sure to download the Add On Packs after you have re-downloaded the "Pinball Arcade Demo".

If this doesn?t work, deleting the old version and then following these steps should certainly work.

This is a onetime issue on PS3 due to a bug that we have fixed regarding PSN updates in our game. This is not an issue on the PSVita version. We apologize any inconvenience.
Click to expand...

I went through the steps yesterday, and they'll result in you being able to play the new tables.