In his appeal filed Monday, Heckman argued that Judge William T. Nicholas had erred by allowing individuals who claimed they were victimized by Young to testify.
The victims included Young's former wife, who testified that he shot her in the head in October 1986 after an argument.
Heckman also argued that the judge should have declared a mistrial when Montgomery County District Attorney Michael D. Marino read a portion of Young's 1987 testimony that criticized what he called "foreign Muslims" and how they manipulated others.
The July 13 jury decision marked the second time Young was sentenced to death; this is also his second appeal. Nicholas will review the appeal.
The state Supreme Court overturned a 1987 death sentence in March. The court ordered a new sentencing hearing after ruling that Nicholas had improperly instructed jurors on how to apply the death penalty.
In May 1986, a jury convicted Young of two counts of first-degree murder in the stabbing death of the Faruqi couple. He was also convicted of aggravated assault in the stabbing of the couple's pregnant daughter, who was in their home at the time of the attack.
Anmar el-Zein required 250 stitches for cuts to her arms and chest. Her baby, a girl, was born a few months later.
Isma'il Faruqi, who was Palestinian by birth, taught Islamic studies at Temple University. Lois Faruqi was an American-born pianist and author who converted to Islam. She taught Islamic art and architecture at Temple.
Young was arrested seven months after the slayings, which caused muchalarm as Islamic leaders speculated that the killings were political assassinations.
Young's defense relied on psychiatrists who testified that he had been a ''paranoid psychotic" who suffered from hallucinations and delusions.
Young said he had heard voices telling him to kill the Faruqis, according to testimony.
Young believed the Faruqis had been forcing Muslim students at Temple to have homosexual relations with them in exchange for scholarships. Young was a convert to Islam.