Any feedback? Was your line LTE enabled?
I also have the same problem with my S3 LTE. This "emergency calls only" or "not registered on network" LTE problem is quite annoying. I read online it has something to do with the phone needing to switch from LTE to 3G quickly to take an incoming call or perhaps when you loose/have weak LTE reception. I don't have all the details, but missing calls and connectivity issues is supposedly a common LTE network problem and the way that the S3 seems to handle it is particularly bad. I drive through one particular area of weak Vodacom reception (on all bands) on my way to work and I suspect this triggers the bug (at least if the phone happened to be receiving or sending data).
Some tips:
1. As said above, make sure you are enabled for LTE (phone 111 or the vodacom self service site) and are using the LTE apn (you should get the right settings via *111# once your line is enabled for LTE).
2. Run the phone in gsm (or wcdma) only mode (which saves on battery too). Keep in mind, if you run in wcdma only mode, you'll also completely loose network connectivity if you leave a 3G reception area. Supposedly there is a way to put the phone in gsm/wcdma auto or wcdma preferred mode (no LTE) using the hidden Samsung service menu - although I haven't tried it.
3. Switch manually to LTE/auto mode when you need high speed. I use a "shortcut" app called "4G Toggle" by "We make better apps" to quickly jump to the right android settings menu (I couldn't find a widget that do this automatically on android 4+. There seems to be no functions in the android 4 API to modify this setting programmatically).
4. I also run a app called "No coverage alert", which warns you if and when this bug is triggered. This could be very useful for troubleshooting this bug.
5. Something I haven't tried yet is to use the normal "internet" apn and not the LTE one and see if the bug still surfaces - although you might not get the full LTE speed (which kinda defeats the purpose...).
In time I hope this resolves itself as Vodacom upgrades their LTE coverage.
Also see these posts (
1,
2 and
3).