A collection of newspapers is seen lying on a table bearing headlines about the prospect of Jim Hacker becoming prime minister. The banner for The Guardian is misspelled as "Gaurdian". However, this may not be a goof as the Guardian has been known for decades for its many typos. (In some circles, it is known as "the Guarniad.")
It would be highly irregular for an apolitical public servant like Sir Humphrey to advise a minister on developments in their own party ("Central House"), such as whether anybody would be nominating to be the next Prime Minister.