No one ever laid an official complaint into the conduct of the police investigation into the Bain murders.
The Police Complaints Authority did a thorough analysis of the police investigation into the Bain murders in 1997 and found that it was satisfactory. In his book David and Goliath Karam criticized just about every aspect of the investigation from the delay in taking GSR tests of Robin's hands to the delays in getting the pathologist into the house.
The authority acknowledges that improvements could be made in a number of areas such as using light metal plates instead of plastic sheeting for protecting the crime scene during the investigation and taking greater care to preserve potential firearm residue as soon as possible. One officer did make a serious error in the rifle measurement but, once corrected in the first trial, this was of no consequence.
Overall, many agents of the Crown carried out a great many tasks in investigating a crime of the worst kind that new Zealand has ever seen in a manner that was quite satisfactory.
Joe Karam's contribution to the Justice system in respect of this has been entirely negative. All he has done is criticize the police on the basis of records made after the fact in an area of expertise in which he has absolutely no experience and in which at times he displays a lack of understanding.
It is easy to criticize and condemn people. If you pull apart any person's average work day you would be able to poke it full of holes and find things that could have been done better or at least argue that if done differently it might have been better. If there is a general public opinion that the original investigation was flawed then this owes its existence almost entirely to the publication and promotion of that idea by Joe Karam himself, who makes sure that he takes every public opportunity to repeat his mantra that the investigation was a "total shambles" as part of a specific propaganda campaign aimed at discrediting the verdict of the 1994 trial. If you allow yourself to pull aside the hyperbole and take another look at the police investigation, take into account that it was 1994, and was in Dunedin and not CSI New York, then you might be able to see that the investigation was actually carried out in a satisfactory manner. It may not have been perfect, but it was certainly not a "total shambles".
The idea that the original police investigation was a "total shambles" is Karam's key propaganda piece and even people who disagree with the retrial verdict have been taken in by it.