The building where the detectives work is called Cope House after the original Hopkirk: 'Kenneth Cope'.
Many of the close ups of Jeff's hands during the series were performed by writer/producer/directer Charlie Higson, because Bob Mortimer's badly bitten fingernails were deemed unscreenworthy. According to Charlie Higson, 'Bob's hands are not that attractive. Mine, however, are quite gorgeous.'
As a character quirk, Jeff Randall is a crisp addict, even packing them to take on holiday with him. Trivia on IMDB