Patrick Quirke’s lawyers claim their client did not receive a satisfactory or fair trial for the murder of Bobby ‘Mr Moonlight’ Ryan.
Quirke, a farmer from Breanshamore, Co Tipperary, was convicted by majority verdict last year, but is appealing his conviction this week.
Bobby Ryan, a local DJ who went by the name 'Mr Moonlight', went missing in June 2011 after spending the night with his partner Mary Lowry.
Patrick Quirke, who had an affair with Ms Lowry, found his body in an underground tank in April 2013.
The prosecution claimed this discovery was staged, and that he killed his love rival in order to rekindle his relationship with Ms Lowry.
Opening Quirke's appeal today, Bernard Condon pointed out that the case was entirely circumstantial, so each piece of the evidence had to be considered by the jury before they could form an overall opinion on guilt or otherwise.
If some pieces of evidence were missing or if some evidence was present but shouldn’t have been, then he suggested it was impossible for his client to get a fair trial.
He described the trial his client received as unsatisfactory.
The first of 52 grounds of appeal presented by the defence today focused on what they claim are significant shortcomings in the pathology evidence.
The hearing, which is being held remotely, is due to take four days.
Reporting by Frank Greaney