Before he walked free from court, Lord Brailsford hit out at the forensic evidence in the case, prompting the investigation by the Home Office Forensic Science Regulator.
The trial heard that just a single particle of firearms discharge residue was found on a jacket seized during a raid on Mr Monaghan's home.
Forensic expert Alison Colley said the particle was insufficient to draw any scientific conclusion, despite previously preparing a report stating the residue was of a similar type to that used in cartridges recovered from the crime scene.
She admitted in court she had formed her conclusion at the request of a detective superintendent involved in the investigation.
Lord Brailsford said: "Miss Colley displayed great candour and said she had been told to file her report in the way she did by a detective superintendent.
"I find this evidence to be disturbing."
He pointed out that the Scottish Police Services Authority (SPSA) which ran Scotland's police forensic services and has now been replaced by Scottish Police Authority, was an independent body distinct from the police.
He added: "If the integrity of the SPSA is to be maintained it should not be influenced by any outside body."
Lord Brailsford also heavily criticised police after a firearms officer admitted that during the raid on Mr Monaghan's home he and colleagues wore the uniforms they had earlier worn to a gun training exercise.
The clothing would have been covered in firearms residue, contaminating evidence.
The judge said: "It was absolutely clear that the search of the house and the jacket seizure gave rise to contamination. I was told the search was, in scientific terms, horrendous, and that is also my conclusion."
The court also heard only one-tenth of a billionth of a gram of Mr Monaghan's DNA was found on the handle of one of the guns used to kill Carroll. The DNA of a lab worker who never touched the gun and worked three floors above where it was stored was also found on it.