When Jessica Pollock is playing the trumpet, the music scholarship is funded by the Endeavour Award provided by an anonymous bequest. The secretary tells Lewis that the only stipulation the benefactor made was that the winner must "give solace to the soul with their playing". It is obvious that the benefactor was none other than Morse--whose rarely mentioned first name was "Endeavour."
Just after Hathaway collects Lewis at the airport, they are nearly run over by a burgundy Jaguar very similar to the one that Morse used to drive, causing Lewis to think for a second that he is seeing a ghost. This is just one of the many references in this episode to Morse's influence on Lewis.
In Russell Lewis's original storyline, the pathologist was a new character called Dr. Woodley. As development on the episode progressed, Laura Hobson was brought back as the pathologist. The producers had wanted to bring back a character from Inspector Morse (1987), but they had realized that, aside from Kevin Whately and Clare Holman, all the regular actors on that series had either died or retired from acting.
It was intended that Chief Supt Strange played by James Grout would appear, either as the superintendent or at least in a transitional scene in a nursing home after his retirement. But Grout was too ill to work, so the character of Strange was written out, and Supt Innocent was created instead.
Kate Jekyll was intended to be a recurring character and, in the longer term, a love interest for Lewis. For various reasons--including Kevin Whately's objecting to killing off Valerie Lewis only to immediately replace her with a substitute character--she never appeared again in the full series.