Are there any hidden dangers?
New Zealand is unique in that it has no dangerous predators or other deadly creepy crawlies. There are 2 or 3 poisonous species of spider but these are very rarely found and their bites although painful respond quickly to treatments.
Swimmers should treat the seas of the western coastline with extreme caution especially for dangerous rips that can trap the unwary swimmer.
Similarly, lakes and rivers can look deceptively calm and safe. Always talk with a local before venturing out and never swim when alone.
New Zealand has many natural hot springs and spas, perfect for easing tired bodies. A rare amoebic parasite that can gain entry to the body through the nose can be found at some sites, so a general rule of thumb is to keep your head above water at all times.
Stay with the main trail when in the bush (New Zealanders tend to use the word 'bush' to describe their forests) Every year a number of overseas visitors over-estimate their abilities and underestimate the conditions to find themselves suddenly lost.
If taking an overnight trail, pay special attention to local weather forecasts. New Zealand weather can change very quickly, even in the course of a day.
So in summary New Zealand is an extremely safe country to travel around and an approach to any situation based on common sense is the main requirement.