Only authorised Marriage Celebrants can conduct legal marriages in Australia.
Members of The Celebrants Network who offer marriages are registered by the Attorney General's department and you can check their registration here
Under the Marriage Regulations 2017 all marriage celebrants must adhere to a Code of Practice for Marriage Celebrants.
If a couple have concerns about the conduct of their celebrant and cannot resolve the matter with the celebrant, there is an official complaints procedure which is detailed here