Lawyers for the Director of Public Prosecutions spent all of Monday attempting to persuade a full bench of the ACT Supreme Court against quashing Eastman's conviction for the 1989 murder of Assistant Federal Police Commissioner Colin Stanley Winchester.

Eastman has spent more than 19 years behind bars for the assassination, but won a major battle in an inquiry into his conviction, which wrapped up earlier this year.

That inquiry, presided over by Acting Justice Brian Martin, recommended his conviction be quashed, due largely to glaring flaws and credibility problems with crucial forensic evidence used to link Eastman to the murder scene.

The inquiry's report is now with the ACT Supreme Court, which must decide Eastman's fate.

Senior counsel for the DPP Jeremy Kirk, SC, urged the three judges to consider the "evidentiary landscape as it now stands" against Eastman, removing the forensic evidence, but adding other available evidence.

He said the judges needed to consider whether that remaining evidence left a "significant possibility" that the jury would not have convicted Eastman.

Justice Steven Rares told Mr Kirk it would take a "big call" to find the guilty verdict against Eastman was safe, given what is now known about the tainted forensic evidence of Victorian-based expert Robert Collins Barnes.

Mr Kirk acknowledged the key hurdle he faced was convincing the court that, even without the flawed forensics, there was not a sufficient doubt or question about the safety of the verdict.

The court spent much of the morning arguing about how it should treat certain secret documents, including the confidential version of Acting Justice Martin's report.

Mr Kirk then set out the criteria that should guide the court in deciding on Eastman's fate, as intended in laws created by the Legislative Assembly.

Mr Kirk then spelt out what he saw as the erroneous approach of the inquiry.

He said it fell into jurisdictional error, misdirected itself, and again criticised the validity of the order creating the inquiry, made by Acting Justice Shane Marshall in 2012.

He said the inquiry's report should have weighed up the remaining circumstantial case against Eastman and assessed it properly.

He also urged the full bench not to take into account Acting Justice Martin's recommendations, including to quash the conviction, and instead simply look at the findings of fact made in the report.

Mr Kirk said the inquiry head had erroneously arrived at his conclusions.

He also noted that Acting Justice Martin appeared to have avoided saying he had a "reasonable doubt" about Eastman's guilt, instead saying he was "fairly certain" but had a "nagging doubt".

The hearing will resume on Tuesday morning in the Federal Court building.

Mr Kirk is expected to continue his submissions, focussing on the alternative hypothesis that Calabrian mafia figures may have killed Mr Winchester.

Eastman's counsel Mark Griffin, QC, will then make submissions to the court about how he thinks it should proceed.