One of the possible models for Sir Humphrey Appleby was Sir Douglas Wass senior civil servant (Wallasey, Merseyside, England, Uk 15 April 1923- 4 January 2017 England, Uk)
Jim Hacker's full name is James George Hacker.
This pilot episode originally had a completely different set of titles and theme music to the rest of the series. However, when it was broadcast they were changed to the more familiar and regular Ronnie Hazelhurst/ Gerald Scarfe theme and caricatured titles. However, the original theme (a brass band composition by Max Harris and titles (non-caricature sketches of the cast) are used on the DVD releases of the series.
The first season of Yes Minister was ready to air in 1979, but the BBC opted to delay broadcast until well after the general election of that year to avoid any accusations of political commentary. This episode was first shown in 1980.