In the first and fifth episodes of series three, Satan claimed that Jill Dando was one of his guises. Tragically Dando was murdered just after the series finished. As these episodes were due to be repeated the following month, the relevant parts were re-recorded so as not to upset or offend listeners. In the edited version of the episodes Satan's guise is Gabby Roslin.
There is a reference to Alastair Campbell in episode 5.2. However, because the episode was recorded before the 2005 General Election, it was necessary for the production team to also record an alternative version of the scene in which Michael Howard was mentioned instead.
According to Andy Hamilton, at the producer's insistence, they also had to record a third version in which the name of Liberal Democrat leader Charles Kennedy was used... just in case the minority party were elected to parliament!
In his one man show, Andy Hamilton's Hat of Doom, Hamilton got the audiences at all of his shows to record the sound of the Battle of Armageddon for the seventh series of Old Harry's Game. The material was not used.
In one episode in which Satan and the Professor go inside Thomas's brain, they see a section in Thomas's brain which contains his prejudices. One of them includes Thomas's view that "Ginger people are bastards." However, it is revealed later in another episode that Thomas is himself ginger.
Source: Episodes 3.4 and 6.6.