The calls were made 18 months before Beckham's trial, while he was in custody on other matters. Police listened to seven to nine calls, Mr Mount said.
He asked that either Beckham's convictions be quashed altogether or a retrial be held at which police who listened to the calls had to give evidence. Alternatively, the sentence should be reduced.
Justice Stevens said Beckham was an admitted drug dealer and the victims of his crime would be punished by a sentence reduction.
Also asking for a sentence reduction for Beckham at the Court of Appeal was lawyer Steve Bonnar. He argued that the eight months Beckham spent on electronically monitored bail was not taken into account at sentencing.
It also emerged Beckham has stage-two pancreatic cancer.
"One of the provisions of the sentencing act is that a court has to have regard to the fact whether there are any factors that would make the term of imprisonment more harsh for a particular person than for an ordinary person," Mr Bonnar said.
It was hard for Beckham to receive the treatment he needed. Mr Bonnar said the Paremoremo Prison lockdown in July had meant Beckham missed a radiologist's appointment.
When arrested in 2008, Beckham was a significant figure in the methamphetamine trade in Northland and Auckland, police said. He was described as a crime boss who made millions in a drug ring he ruled ruthlessly.
Officers found 112g of methamphetamine in his car and 252g buried next to his driveway, and $856,720 in a car and in Beckham's house.
Assets and cash worth more than $10 million were frozen by the High Court.
Two late-model Ford Falcons were among assets seized - one with the registration plate B4DBOY - as well as a fishing vessel called Unity.
As the presiding judge, Justice Stevens reserved the court's decision.