In real life: Gaiman and Pratchett did a radio interview when the book came out, and slowly realized that the interviewer wasn't aware that the book was fictional, and thought they were a couple of religious kooks writing about what they thought would be the real apocalypse. They spent the rest of it viciously trolling him.
The fake member list for the witchfinder army.
The really funny part? The member list was, by the end, named after inanimate objects. Shadwell could have easily filled in names with actual names by cracking open an ordinary phone book.
AND the insistence on Hell using whatever their target is watching or listening to as a way of communicating. Which means that Freddie Mercury suddenly starts singing messages at Crowley.
This becomes a bit of a Brick Joke near the end of the book when Crowley's car is restored from the flaming wreck it turned into.
Crowley inserted a cassette labled "Handel's Water Music", and it stayed "Handel's Water Music" all the way home.
Newt showing his Witchfinder ID to the American soldier.
"What's this here", he said suspiciously, "about us got to give you faggots?" "Oh, we have to have them," said Newt. "We burn them." The guard's face broadened into a grin. And they'd told him England was soft. "Right on!" he said.
The four other Bikers of the Apocalypse picking their names. "You can't be answer phones!"
Newt discovering that not only did Agnes predict him and Anathema having sex, but many of the Devices down the centuries have written in advice.
For some reasons, this troper's unofficial book group found the confusion over who's name you swear at very funny.
Shadwell talking to Madame Tracy. Everything about Madame Tracy.
And everything about Shadwell.
The Buggre All This Bible. What really pushes this one from amusing into laugh-out-loud hilarious isn't so much the text of what was inserted, but where it was inserted. To wit:
2. And bye the border of Dan, fromme the east side to the west side, a portion for Afher.
3. And bye the border of Afhter, fromme the east side even untoe the west side, a portion for Naphtali.
4. And bye the border of Naphtali, from the east side untoe the west side, a portion for Manaffeh.
5. Buggre all this for a Larke. I amme sick to mye Hart of typefettinge. Master Biltonn if no Gentelmann, and Master Scagges noe more than a tighte fisted Southwarke Knobbefticke. I telle you, onne a daye laike thif Ennywone half an oz. of Sense should bee oute in the Sunneshain, ane nott Stucke here alle the liuelong daie inn thif mowldey olde By-Our-Lady Workefhoppe. @*"AE@;!*
What makes it funnier if your listening to the audio book, is the narrator getting increasingly more and more angry as he reads the line.
6. And bye the border of Ephraim, from the east fide even untoe the west fide, a portion for Reuben.
Not to mention the three extra lines in Genesis:
25 And the Lord spake unto the Angel that guarded the eastern gate, saying Where is the flaming sword which was given to thee?
26 And the Angel said, I had it here only a moment ago, I must have put it down somewhere, forget my own head next.
27 And the Lord did not ask him again.
Crowley trying to conceptualise good luck: "a blessi- a godse- a windfall."
"I glaim gis oteg in der gaing og deró" he paused. He took the knife out of his teeth and began again.
The EULA for the (presumably Apple) computer Crowley bought, and what he does with them. (He sends them Below to the department that draws up contracts with a sticky note attached saying only "Learn, guys.")
Aziraphale possessing a televangelist mid-speech about the Rapture and proceeding to give the audience a blunt Reason You Suck Speech, saying that Heaven honestly didn't care about humans and didn't have a 100% chance of winning, and inevitably humans would be demolished in the upcoming war between Heaven and Hell. Then he notices exactly where he is:
Most of the sequence of Aziraphale possessing people, actually.
Aziraphale's one-sided conversation with Crowley's answering machine, in which he's rather preoccupied and as a result completely fails to notice he's speaking to a recording. Culminates in this exchange:
Aziraphale offering Crowley the obligatory We're-About-To-Get-Creamed-So-Let's-Make-Amends concession that, deep down, the demon's got enough goodness in him to be worthy of liking ... and then Crowley turning the cliche around and saying Aziraphale is worth bothering to like because, deep down, he's a bit of a bastard.
On his way to investigate Lower Tadfield, Newton Pulsifer encounters a flying saucer.
"You do know you could find yourself charged with being a dominant species while under the influence of impulse-driven consumerism, don't you?"
It's mentioned that the only person to call Pepper by her real name is her mother... and Greasy Johnson and his gang. When they're feeling particularly brave. And they're absolutely sure she's out of earshot.
When the Four Horsepersons walk into a biker bar, some bikers there ask them about their jackets, which say "HELLS ANGELS" on the back. When asked what chapter they belong to, Death takes him literally and replies "Revelation, Chapter Six".