We are both Elites, I have been for many years.
There are three things that I think the airline could do much better, and complaints to Air NZ are generally a waste of time, you are labelled as a complaining customer:
Firstly, it is often not hard to work out when a service will be delayed or cancelled, by working backwards from your flight. But the notification is usually very late.
Secondly, we don't trust the airline to get us there. We now leave for Auckland the day before for an international connection. But what gets us is the lack of help when things do go wrong. Any reasonable person would expect that an Elite on an expensive Business Class fare would get the help they need, in a timely, hopefully proactive manner. But usually we are on our own in a first come first served situation. A dedicated phone line with knowledgeable staff would make all the difference. Proactive help would be even better.
Thirdly, the treatment we receive is extremely variable. It can be excellent, or mediocre. It is not hard to treat Elites like they are Elite, particularly in Business Class.

The clear indication of how Air NZ regards its Elites is the service on an ATR, Elites (usually in the back rows) are deliberately served last.
Some meaningful interaction through Flyertalk would be really useful.