"Three years ago, my QF flight diverted to Nadi because both destination AKL and CHC were closed due to fog. The crew seemed to indicate that it was that unusual in fog season. But, outside of SCL and EZE, there are almost NO Cat II and Cat III approaches in Southern Hemisphere".
It isn't all that unusual to end up at Nadi when en route US-NZ. Over the years this has happened to me 5 times. Usually it isn't because AKL and CHC both have fog - it is because AKL does and CHC Wx indicates that there might be in 5 hours time. When it happens they get you off the plane reasonably fast, but then you have to wait for a new crew to arrive from somewhere. Compared with the BNE experience though, they don't do a bad job of moving people into hotels.
Ohakea is not limited to NZ, as someone has said in this thread, but when there are a group of diversions there - as happened once last year (7, I think) - the pax are even worse off than those in BNE last week. There is no infrastructural support to get them off the planes at all - and no stocks of food and drink to put aboard.
There have been some close calls over the years. The most famous being the UA flight that landed at WLG when they realised half way to CHC that they didn't have enough fuel for a missed approach at CHC or to get back to anywhere else that could take them.