The new filing also repeated other arguments that were rejected a month ago by the mid-level Superior Court, including a claim that Sandusky's lawyers lacked sufficient time to prepare and that a prosecutor improperly referred to Sandusky's decision not to testify.
"This is a notorious case," wrote his lawyers, Norris Gelman and Margeaux Cigainero. "It is a case that tests the limits of our ability to live up to the promise our constitution makes that even in the worst of cases, a fair trial will be afforded."
Gelman said Friday that it typically takes the Supreme Court two to seven months to decide if it will grant a petition for allowance of appeal. If it does, the justices will establish a briefing schedule.
A spokesman for the attorney general's office, which prosecuted Sandusky, declined comment.
The 59-page petition argues that Judge John Cleland's decision not to issue the "failure to make a prompt report" jury instruction was catastrophic to the defence strategy.
"It cut the heart out of (Sandusky)'s main defence," they wrote. "Just as the court could not deny (him) the right to forward such as defence, it had no right to dilute it so seriously by refusing the instructions."
Gelman noted Friday an announcement this week by Penn State that it has reached settlement terms with 26 young men, agreeing to pay them nearly $60 million over claims of abuse by Sandusky.
"My guess is that the jurors never dreamed that the complainants would become multimillionaires," Gelman said.
The defence lawyers said most of the eight young men who testified against Sandusky waited years to disclose the abuse, although one told his mother about showering with Sandusky the same day. The others ranged from two to 16 years, they wrote.
Cleland said he would not issue the jury instruction because he believed research indicates delayed reporting is not unusual in child sexual abuse cases, so a delay would not necessarily indicate dishonesty.
Also at issue in the latest defence petition is Cleland's decision to tell jurors to weigh Sandusky's character evidence against all other evidence.
"The jury was given no burden of proof or standard by which to weigh character evidence against the other evidence in the case," the defence lawyers wrote.
Sandusky's lawyers said repeatedly before the June 2012 trial that they needed more time to go through a large volume of material from investigators, but during a post-sentencing hearing attorney Joe Amendola said that even after the trial he had not discovered anything that would have altered his approach.
"His attorney operated blindly when he should have at least had the confidence he had read everything that could be involved in the trial of the case," Sandusky's petition says. "Lacking that confidence, he was forced to go forward."
Sandusky, 69, a former Penn State assistant football coach, was convicted last year and is serving a 30- to 60-year state prison sentence.