Nether portal blocks facing east or west have incorrect rotations after upgrading old worlds

The bug

I recently converted a world from beta to the latest version and I saw a problem with the nether portal. The rotation of the portal was not correct.

More information can be found in this comment by Jess Edward.

How to reproduce

1. Load an instance of Minecraft beta 1.7.3, create a new world, and construct a nether portal
2. Exit the world and launch the latest snapshot or release of Minecraft
3. Upgrade the world and look at the nether portal