We tried to use one of our existing options the other week, to catch a show we forgot to record (TVNZ On Demand via the PS3). It was unusable to the point that we had to give up 30 minutes in.
Who is your ISP? There have been a number of people say TVNZ and TV3's service is terrible on Slingshot.
Telecom. I have no qualms with their performance generally.
The TVNZ On Demand experience is terrible. Not only does the UX leave a lot to be desired, but video playback stopped every few minutes, taking a few seconds to recover. At about 30 minutes in, playback stopped again but never recovered.
Are you using the Telecom DNS servers? Do you have the latest version of Flash?