Lots in the series, and especially prevalent in the comedy of errors integral to the plots of The Galileo Affair and The Bavarian Crisis. One of the more specific example is Tom Stone who, when tasked with making paper money due to his knowledge in making waterproof dyes, promptly putJohnnyCash on the 20-dollar bill.
Pictures for one dollar bills include male deer (a buck), fivers have a pair of hands kneading dough, tens have a loaf of bread. Get it?
The Baltic War has Melissa Mailey freaking out after Harry Lefferts has bombs planted on several famous London landmarks like the London Bridge and the Globe Theatre. She's further enraged when Harry dismisses his bombing of the Globe Theatre with a nonchalant "Jeez, Ms. Mailey, ease up some, willya? It ain't like we're talkin' about Grauman's Chinese theater in Hollywood, y'know."
All in all they do quite a number on invaluable historical landmarks. In 1632 they drive a small Spanish army into a nearby castle, then napalm it the next day. Passing mention is made that the castle might be important, but the concern is dismissed. That castle? A UNESCO World Heritage Site with "lasting and universal significance". Considering it attained that listing in 1999, it seems probable that its significance was precisely why it got destroyed in a book published in 2000.
Most of the short story "When the Chips are Down," featuring the four Dungeons and Dragons nerds trying to cook potato chips for the whole town in time for Christmas.
The entirety of the short story "On the Matter of D'Artagnan", in which Cardinal Richelieu tries to locate and gain the loyalty of the hypothetical historical person Dumas based D'Artagnan on. Complete with Richelieu staring at the pictures on the videocassette boxes of two different movie adaptations of The Three Musketeers, musing on if he likes how Charlton Heston or Tim Curry portrayed him better.
In The Bavarian Crisis, "the prince formerly known as the Cardinal-Infante" has the idea for a bold action that will make great propaganda for his new regime. His advisors are aghast, since it involves him risking his life in one of the still-somewhat-crude airplanes. He points out, "Just think of the songs. The poems. The Harlequin Romances." (They're still aghast.)
The single casualty on the Grantville side to the Croat attack on the town was a woman injured when a black-velvet portrait of Elvis was shot off the wall and fell on her. In the Ring of Fire short story "Between the Armies", it is revealed that a downtimer, Monsignor Giulio Mazarini, was in the room. Not knowing better, he mistakes it for an icon and asks, "What saint is this?"
In "Diving Belle" from Ring of Fire II, the story of the church bells of Delsbo.
Eddie Cantrell getting drafted in "In the Navy".
From 1634: The Baltic War
Jesse: No, I've got plenty of other things to attend to. And participating in another argument over machine guns ranks somewhere below getting a colonoscopy, in my book.
Tornstensson: What is a colonoscopy? And how soon could we have one deployed against the Ostenders?
In the first novel, the D&D boys gush about Frank Jackson's tactical planning of an imminent battle and name drop The Duke Of Wellington, leading to this exchange:
Frank Jackson (gruff tone): So who the hell is Wellington? [beat] Jeff Higgins (appalled): He's the guy they named your favorite boots after. Frank Jackson (now impressed): Oh, him. Good man! Whoever he was.
In the first Grantville Gazette, "The Rudolstadt Colloquy", Secretary of State Ed Piazza is attending the colloquy, bored out of his mind and doodling in the margins of his Concordia Triglotta with a pencil when he meets Leopold Cavriani when he sees the latter was bored out of his mind and doodling in the margin in pen.
In 1632, when some of the mercenaries are put in WANTED-DEAD and advised to leave American territories before July 5, the mercenaries' commander complains about the fact that the "American territories" part is unclear. Mike Stearns just stares at the commander. A few months later, the commander has found a job. In Russia. He figures that it would be far enough.
"The Ram Rebellion" has Brillo, an unusually intelligent ram with terrible wool who becomes an in-universe Memetic Badass and Memetic Molester though broadsheet stories about his supposed exploits.
In 1633, Francisco Nasi uses the forged histories a book smuggler supplies to the French to claim there are gold deposits in the Everglades. In other words, he basically sells them Florida swampland.
Also in The Saxon Uprising, when Gretchen forces Krenz to give a straight answer on whether they could hold Dresden against the siege.
Eric [Krenz] rose, strode to the door, plucked his hat off the hook, jammed it on, and came back to the table.
"I feel better now. Donít ask me why the hat makes a difference. It just does."
From 1635: The Cannon Law, while they're trying to get the Pope out of Rome, he suggests sheltering from the demolition of a gate in some nearby granaries. Ruy's response:
"Did not I, Ruy Sanchez de Casador y Ortiz, say that God would aid us? His personal vicar on Earth shows us the way!"
Frank Stone wondering if there are any ninjas in Venice:
There would certainly be a market for their services. He imagined ads in the Ninja Times of Japan: "Come to Venice for the most lucrative working holiday of your life!"
The first Ring of Fire anthology features, among other things, Santa Pappenheim. That is, the prematurely white-haired General Pappenheim is inadvertently shanghaied into playing Santa Claus for German orphans while trying to deliver a covert message to Julie Sims, who he thinks is a Jew named Lee.