Lawyers for Fred McClenaghan claimed his hopes of proving he never intended to kill Marion Millican were dashed by protocol breaches in examining the hair-trigger antique shotgun used.
They also argued that his responsibility was diminished by mental illness and coming off anti-depressant medication.
McClenaghan, 51, is seeking to overturn his conviction for murdering Mrs Millican at her workplace in Portstewart, Co Derry in March 2011.
The victim, a 51-year-old mother of four, was shot in the chest and died at the scene.
She had been in a relationship with McClenaghan which ended months before the killing.
During the murder trial, her husband told how they had been trying to rekindle their marriage at the time she died.
Ken Millican described finding his wife's body on the floor of the laundrette on the day of the killing, and his failed attempts to locate a pulse.
The weapon used was an antique, double-barrelled shotgun which dated back to the late 19th century.
McClenaghan, formerly of Broad Street, Magherafelt, is serving a minimum 16 years in jail for murder.
His case has always been that the gun went off unintentionally during a struggle in the laundrette.
Handcuffed and flanked by prison guards, he was escorted into the Court of Appeal to hear his legal team begin their challenge to the conviction.
Members of Mrs Millican's family were also present for the opening of a scheduled three-day hearing.
Defence QC John McCrudden claimed serious flaws occurred during testing to establish if his client's claims could be right.
"This was his only hope," the barrister contended."His best chance, and that which he had a reasonable expectation to rely on, was for the state to have handled that gun correctly."
Instead, according to Mr McCrudden, the process was wrongly carried out.
"This was given for proper forensic examination and the very antithesis of this occurs because they breach the central regulations."
The three appeal judges, Lord Justice Girvan, Lord Justice Coghlin and Mr Justice Gillen, were told it was the potential piece of independent evidence which could have backed McClenaghan's version of events.
Everything else was against him, including sympathy for the victim and details being disclosed of his previous alleged violence towards her, the court heard.
"He was saying the gun went off accidentally, and this evidence was capable of saying this gun was in such a vulnerable condition that it was prone to going off accidentally by a jerk or a movement," Mr McCrudden added.
Dealing with the alleged diminished responsibility point, the barrister said McClenaghan had been prescribed anti-depressants - but was effectively drug-free on the day of the killing.
He took issue with how the trial judge handled a defence medical expert's assessment of the defendant's mental state at the time.
McClenaghan's legal team claimed a defence toxicologist was wrongly excluded from commenting on the substantial mental impairment allegedly caused by coming off medication before the shooting.
But Richard Weir QC, for the prosecution, argued that the trial judge only placed a small limit on his evidence after becoming uncomfortable with his degree of expertise in that area.
Pointing out that other medical experts testified on the issue, he told the court: "The defence were not improperly deprived of any advantage from that evidence."