Picture 38Facebook’s iPhone app is getting a few much-needed touchups today.

It now handles push notifications, so you’ll automatically get messages on your phone telling you if you’ve been tagged in a photo or note. Before, you’d have to be logged in or constantly checking your e-mail for messages and wall activity. You could even conceivably use Facebook’s inbox as an alternative to text messaging if all the people you need to reach are in the social network.

Another addition to the latest version is contact syncing, so you can import Facebook friends into your address book. Android’s latest version also supports this — Google was demoing it yesterday when they launched the Nexus One.