Will I need to move app updates to SD card in Android 4.3? If I move a certain app to SD card (from App Info page), what happens when Play Store installs that app's update? Will the update automatically go to SD card, or will it go to internal storage and I'll have to move it to SD card again?
From my experience with my Droid after this functionality was added to Android, updates "go" to where the app is. That is, I did not need to re-move the app to the SD card after an update. As far as I know the functionality for that has not regressed. (Actually, I don't think much work has been done on it at all. Google would like for phones to just have internal storage.)

That said, there's probably more chance of something going wrong with an update in that scenario. You may find occasionally that you have to move an app back to internal storage to update and then move it back to the SD card. Or possibly re-install. But it's probably rare.

I don't currently have a device with 4.3 and an SD card, so this is a bit of conjecture based on my experience with an older version of the OS. Caveat emptor.