Shooty and Bang-Bang were inspired by the title characters in Starsky and Hutch (1975). Douglas Adams' impression of this show was that the characters cared too much to shoot people, so they crashed their cars into them instead.
The incidental (background) music during the Deep Thought scenes sounds a lot like the incidental music used in Doctor Who, especially State of Decay: Part One (1980). This is because Paddy Kingsland did the music for both, and they were filmed at about the same time; he used a lot of the same musical elements in both.