In 1950 the reverse design used for New Zealand half crowns underwent some small changes with both the old and new design being used in 1950. Such a change is not unusual, with many of New Zealand's predecimal designs undergoing at least one small change.
The exact reason for the design change is not clear but it was likely to improve die life: possibly the move to cupronickel coinage in 1947 necessitated the changes due to the harder alloy. Regardless, the change is easy to spot: on the older design the designer's initials KG are close to the diamond directly above while on the newer design the designer's initials KG are far from the diamond directly above. Neither variety is rare.
In 1956 the portrait of Queen Elizabeth II used on New Zealand's coins was updated to more prominently show a shoulder strap on the Queen's clothing (p72, Pepping, New Zealand History Coined, 2017) - this change occurred across all denominations but the old design was also used in 1956 for some pennies and threepences. Although no catalogues report it, there are reports of the old design being used on a very small number of 1956 halfpennies.
Jerome Remick reported the existence of at least one piece which underwent thorough testing and was found to be genuine. He also estimated that perhaps 200 such coins may exist (p461, Remick, British Commonwealth Coins, 1971), although the whereabouts of the reported example or the existence of any other pieces is now unknown: presumably the variety not being listed in any catalogues has left it and other examples as unattributed.
The Royal Mint was extremely busy in the late 1960s - striking enough predecimal coins to last until Decimal Day in 1971; striking new decimal coins that were slowly being phased in 1968; the various contracts that it had for overseas coinage and the gradual relocation of the mint to Llantrisant in Wales. Given all of what was going on it is not surprising that a number of error coins date to this era. One such coin is a 1969 New Zealand 50c piece struck on a British penny planchet.
The 1969 New Zealand 50c piece struck on a British penny planchet is a particularly obvious wrong planchet error given that the colour is incorrect: a New Zealand 50c piece should be silver-coloured cupronickel while British pennies are a brown bronze-like alloy. The planchet sizes are similar but different enough: the 50c piece should be 31.75mm across, 2.33mm thick and 13.61g while a penny should be 30.8mm across, 1.5mm thick and 9.1g - certainly of a similar enough diameter to be struck well enough, though the one known example shows some weakness in the details of the Endeavour (probably due to the lower thickness) and some fish-tailing on the legend (probably due to the smaller diameter).
Among the many different mules struck at the Royal Australian Mint in the 1970s is the 1978 Australian 20c struck with a Fijian 20c reverse. There is no question that these coins were struck at the Royal Australian Mint, as it was responsible for striking both Australian and Fijian 20c pieces in 1978, but beyond that, details are scarce.
Wrong planchet errors are fairly uncommon in modern times as both mints and security companies have equipment that should identify coins which do not meet specifications. In any case, a small number of Australian $2 coins were struck with 10 euro cent planchets, which is especially impressive given that the coins should weight 6.6g but the planchets weight just 4.1g. None of the known coins are struck well enough to show a year, but a number of pieces have reportedly been discovered since 2012 (Eigner, https://www.drakesterling.com/australia-two-dollar-struck-on-foreign-planchet-pcgs-au55-47101599).