The Ian Rank-Broadley portrait of Queen Elizabeth II underwent multiple small changes in the course of its use from 1999 to 2019, but especially so in the period just after its introduction. In 2001 on some denominations the designer's initials IRB under the Queen's neck changed from a sans serif font to a serif font. The 2001 $2 was one of the affected denominations, with the first coins being struck with the designer's initials being in a sans serif font and spaced out, and the remaining coins being struck with the designer's initials R and B being joined at the base and all in a serif font.
The small change was likely done to improve die life, and the initial IRB spaced design is less common in circulation, though neither variety is rare. The IRB spaced variety accounts for approximately 19% of circulating coins and the IRB joined variety accounts for approximately 81% of circulating coins.
On 11th November 2020, photos of a PCGS slab containing a 2020 Mob of Roos $1 muled with a 10c obverse die were posted on a Facebook error coins group. The slab in question was https://www.pcgs.com/cert/40222602 and showed a 2020 Mob of Roos $1 with a heavily clashed 10c obverse (part of the lyrebird are visible around the Queen's head). It was reported as having been discovered in a mint bag.
Currently it is the only known example and there have not been any public sales.
Various catalogues report a New Zealand a 5c piece that was struck with a New Zealand obverse muled with a Canadian reverse (p21, The John Bertrand Catalogue of New Zealand Coin & Banknote Catalogue, 2014). The catalogue itself does not specify which Canadian reverse: a Canadian 1c from the time had more or less the same diameter (19.1mm compared to 19.43mm for a New Zealand 5c piece) though it is reported that it was actually a Canadian dime/10c reverse die.
The circumstances in which it was struck and found are unknown but the Royal Canadian Mint struck New Zealand coins in 1981 - it is likely that the mule was a deliberate fabrication by mint workers. Other similar mules exist from the era.
There have been no known recent public sales of the New Zealand 5c obverse/Canada dime reverse mule.
A number of 2008 5c pieces have been observed with double rims around the obverse and reverse - besides the normal rim there is a smaller, lower rim inside of the normal rim. They are not overly common however they are not rare. The double rim has led to speculation that they may be mules with a 1c obverse die, however the double rim appears on both sides of the coin, and no 2008 1c pieces were struck, so there would not have been any dies with which there could have been a mix-up.
The explanation that has been given is that some of the pre-rimmed blanks used to strike 2008 5c pieces had a slightly wider than normal rim, which, when struck, did not fully align with the rim on the die, thus leaving a slight overhang which manifests as a second rim.
The introduction of the new bronze halfpenny in Great Britain in 1860 saw many different obverse and reverse die iterations produced and used in an attempt to get a satisfactory die life. One of the major design changes was to replace the beads around the rim of the obverse and reverse with denticles/teeth that ran into the rim. Clearly there was not a distinct transition however as there is one known 1860-dated halfpenny that was struck with Freeman obverse 2 (denticles/teeth) and Freeman reverse A (beads) which is classified as Freeman 260C. The coin in question shows a die crack through the top bar of the T in VICTORIA that runs parallel to the vertical stroke.
The single known toothed/beaded border mule was a part of the Laurie Bamford Collection and was also sold by Dix Noonan Webb as lot 208 in its February 12th 2020 auction. There has only been a single known example for many years but the existence of another example cannot be discounted.