The 22-year-old is using a ruling by the Supreme Court that suspects must have the right to have a lawyer present when being questioned by police.
Papers lodged in court note that when Mitchell was interviewed following Jodi’s death he was only 14-years-old and had no legal representation.
Mitchell claims the interview was used to provide crucial corroboration for the Crown’s circumstantial case against him.
The papers also refer to a previous court ruling which described the behaviour of police as “outrageous”.
Today (Thur) defence lawyer Margaret Scott QC asked the Court of Criminal Appeal in Edinburgh to allow a new challenge.
But advocate depute Lesley Shand QC, for the Crown, urged judges not to allow the new appeal as it had come too late.
Ms Scott said the point of the appeal court was to remedy miscarriages of justice and the court had a wide discretion.
She insisted that the new challenge could be heard because it had been lodged in court before the decision in Mitchell’s sentence appeal, so the case was still live.
Lord Hamilton, sitting with Lords Osborne and Kingarth, will issue a ruling at a later date on whether there should be a full hearing about the rights and wrongs of the 2003 police interview.
14-year-old Jodi’s body was found naked, bound and mutilated in woods beside a path in Easthouses near Dalkeith, Midlothian.
Mitchell was locked up for life in 2005 and ordered to serve at least 20 years for the murder.