They say his conviction - for the murder of a 12-year-old girl - was based on bad science, or perhaps even fraudulent science, carried out by a former Philadelphia crime-lab worker who was later disgraced for having claimed a college-level science background when she had never finished junior high.
Over eight years, she gave "expert" testimony in dozens of cases, including two that sent men to the electric chair.
Others familiar with the case, however, remain equally certain of Thomas' guilt.
Despite high-tech equipment unheard of in the 1960s, 21st-century forensic science still suffers from some of the problems that left so much uncertainty hanging over Thomas' conviction. Veterans of the field say that too often, investigators don't approach a crime scene objectively or evaluate evidence in a scientific way.
Bias creeps in, the experts say, when investigators and crime-lab technicians see themselves as working for just one side.
Thomas' conviction was based entirely on science - or what was considered science.
The victim, a sixth grader named Edith Connor, was last seen on a Sunday morning in late September 1964. She left on an errand to the local Laundromat and never returned.
Two days later, on a rainy afternoon, some boys found her 5-foot-2, 103-pound body in a narrow alley that ran behind her West Philadelphia home on Sloan Street near 40th Street and Girard Avenue. Her blue jeans and diamond-patterned pullover sweater were torn. Her shoes and socks were missing.
Thomas lived and worked just 50 feet away. He was separated from his wife, was new to the area, and had several assault arrests on his record.