A number of "gaps in the evidence" in the prosecution against Coulson were highlighted by his lawyer in his closing speech at the Old Bailey.
Among them was the failure by police to fingerprint members of the royal household to check if one of their number, and not unidentified police officers, was the source of royal directories sold to the NotW, jurors were told.
The prosecution also kept evidence of the extent of former royal editor Clive Goodman's phone hacking from the jury, leaving it to the defence to expose it for the first time, the court heard.
Coulson, 46, is on trial accused of conspiring to hack phones and conspiring to commit misconduct in a public office by agreeing with Goodman to pay for two royal phone books.
His lawyer Timothy Langdale QC, told jurors: "Operation Weeting commenced in January 2011 as a high profile investigation and attracting a high degree of public interest and media scrutiny.
"It must have been important that it would be a rigorous investigation.
"We suggest as far as Mr Coulson is concerned it has been none of those things -rigorous, open-minded or fair.
"Case theories have changed at a moment's notice once they have been exposed as impossible.
"Criticisms of the police investigation have been brushed aside for blame to be cast elsewhere, often in News International's direction.
"It's almost as if the juggernaut must keep moving."
Mr Langdale told jurors that it was their responsibility to "do what the investigation so often failed to do - which is scrutinise, analyse, and come to a fair conclusion".
Coulson, 46, of Charing, Kent, along with six co-defendants denies the charges against him.