That’s the Australian coat of arms, not the South Australian one.
You are right, I got to looking and this was the ONE coin (of course) that got the coat of arms wrong.
http://www.australianstamp.com/Coin-web/aust/cwealth.htm
The design for the coat of arms on 1938 coinage contained mistakes. It was intended to update the coat of arms from the original 1906 to the 1912 design which was correctly placed on the 1934 issue of notes. Unfortunately, the wrong coat of arms of South Australia was used - a rising sun and three stalks of wheat instead of the Piping Shrike. The traditional star atop the shield was also wrong; it was replaced with an oversized crown.