The body found in the mire at the beginning, of a man who'd been strangled 2000 years previously, is a clear reference to Tollund Man, who was found in a bog in Denmark in 1950, 2300 years after his death, with a leather garrot about his neck.
Sheila Hancock's character, Dowsable Chattox, is named after 'Old Chattox' one of the women charged with witchcraft in the famous Pendle witch trials. Like Dowsable, she was an elderly woman supposedly gifted with the power of foretelling the future.
When Joan Thursday is asked by her father why she isn't at work on this particular afternoon, she replies, "Half-day - early closing", a reference to the practice of many British shops and stores, still quite common in the 1960s, to close for one afternoon during the week (in addition to being closed all day on Sundays). This practice was largely abandoned during the 1970s, and entirely abandoned after Sunday trading became lawful.
Nigel Warren is seen wearing a CND badge, and there are references in the story to the Aldermaston march, where many members of the Campaign for Nuclear Disarmament converged on the nuclear power plant at Aldermaston to protest its existence and Britain's nuclear industry. The tripod symbol of the CND was also adopted by American protesters against the Vietnam War.
Discussing with Bright the incompetent handling of the Laxman case five years earlier, Thursday refers, with obvious distaste, to his former colleague Detective Sergeant Lott. This was the corrupt policeman played by Danny Webb in the pilot episode of "Endeavour" in 2012, a character forced to leave Oxford by the end of the story - although he re-appears in "Exeunt", the very last "Endeavour" story.