I suspect the trick will be to find things that seem normal to people like us, and are thus authentic, but are not what people in the so called real world experience very often.
I have some constraints on my best stories
a) because of confidentially
b) I would no longer be the centre of attention at parties if people think I stole my anecdotes off a TV show
A first thing to know is how the story begins
So imagine you are studying the formaiton of galaxies in the after the dark period following the big bang. It's relatively obvious that this involves solving a complex array of partial differential equations, (for a given value of 'obvious'). As it happens this involves the generation of a seriously impressive number of random numbers.
So some guy who sounds like Hugh Laurie when he's using his English accent phones you out of the blue. Whilst you're working out how he got your unlisted number you find yourself in the following conversation
HH: "You are studying galaxy formations, Alexei ?"
Alexiei "Yes, but who.."
HH:"That's good. We like people who do that"
Alexei: "are you interested in Cosmology ?"
HH: "No"
Alexei : "what do you want ?"
HH: "I want to know how to weigh a large passenger Jet"
Alexei: "what, why ?"
HH: "You do need to tell me this, and if I could ask you to tell me now please, I would be
most grateful"
A: "I guess you find a slope, take the sine of the angle and multiply it by the force necessary to hold it in equilibrium"
HH: How do you change the value of the constant pi ?
A: Who are you ?
HH: None of your business
Alexei holds the phone away from his head and stares at the phone as if he expects it to bite him.
HH: I would, if possible like to encourage you to answer me
now please.
A: You mean change it in
C++ by casting away constness ?
HH: By using circular brackets and the mutable type ?
A: No, that's shit man, you a C programmer ?
HH: I'm so glad you got that part right, I would have been
disappointed f you'd used brackets.
A: What is this about ?
HH: Banks like people who model galaxies in
C++. My role is to find such people and ensure money happens to them.
Real money, or if you are good as people tell me,
complex money.
Those questions are real interview Q's for investment banks, though of course I ask harder ones than that

And yes banks do like people who model complex systems using that type of math, and of course they expect them to be wise in
C++ a language that is so difficult to use that everyone who knows it has read the story that it was invented as a joke, just to torment people.
http://artlung.com/smorgasborg/Invention_of_Cplusplus.shtml
Although I've hammed up the HH in this outline, I have run conversations not very different to this, on unsuspecting postdoc students.
Another one from my own career when I was on the statistical arbitrage desk of a very large bank where we were "not in any way capital constrained". Why, you ask, am I not faboulously rich ?
Read on...
Three are two types of currency. Some are like Dollars, Pounds and Euro, having both dollars and cents, pounds and pennies etc.
Others are like Yen or Lira and inflation long ago killed the fractional unit.
So which one is the South African Rand ?
You don't know do you ? (don't cheat by using Wikipedia.)
So we were running multi currency , multi stock stat arb, and most of the traders job was just doing the trades that the computers told them. In less developed markets at this time you couldn't do much volume electronically, so we were doing pairs between a large range of currency / exchange / stock combinations, so many of them that two things happened:
1) The traders had no intuition for what the 'right' price for any given stock might be , and and so had no hope of spotting bad numbers.
2) the computers had no clue either because no one had spared the time to put in place sanity checks.
We were protected however by the systems at the exchanges, which would not accept a price that was too far wrong.
We were were having issues calculating our exact profit and loss on a daily basis. That's actually quite a common issue, some trades don't quite go through, or occasionally people put in a wrong number into the trade capture system.
However this was one of the world's largest retail banks, and the P&L of our one desk varied from one day to the next by a greater amount than the P&L of that whole retail operation.
At some level, we were worried about that, but not really as worried as someone in the real world might expect. As the Chief Exec of our division explained to me over wine, "if a girl on a cash till was $50 out she'd be fired, maybe in prison, we seem to have mislaid ten million times that", but as this was not all the scary (in this context) he wished to praise me for hiring a particularly pretty girl programmer, who just happened to have been sat very close to him. This had not been a trivial task for me.
He was a smart guy, and he'd somehow managed to get the audit manager for our group in the same trading bonus pool. To a real person that won't sound odd, but actually some here won't believe that was ever possible and I believe it's now a serious crime since her job was to stop us being bad with the banks money.
We said the computers worked. Which was true. Somehow I'd managed to say that in a way that was unquestionable , and so audit and their friends had the situation where the numbers all added up but were horribly wrong and random from one day to the next.
Turned out that the traders had each randomly guessed whether the Rand was dollars and cents or just Rand. So some were over pricing their trades by a factor of 100
Some were pricing trades at 1/100th, and by luck some actually got it right.
That means the books had the right number of shares in the pot, but we'd sometimes be selling at a penny things we'd bought at a dollar, and vice versa.
I had to sort that out, was not pretty.
The meeting where we discussed this was held in a former communications room. Banks have a
lot of wires, really lots. It had reached the point where no more wires could be put anywhere because the holes, conduits et al were all full. So a big reload had happened, and they'd stripped out a load that turned out not to be connected to anything (probably). So we annexed a former comms room for meetings, and it was a really cool Blade Runner environment, lots of bits of hardware still nailed to the wall, big cables that had been cut with bolt cutters and a few impressive burns.
Banks are typically really shit about their wires, The wiltess fools who run JP Morgan's technology in London have had real problems getting reliable electricity to the trading floor, because they understand golf better than technology. It was so bad at one point that my guys who had to visit JPM's office to look after the GiltSwan, were forbidden to touch certain bits of network hardware because in my opinion they were physically dangerous. Their aircon was shit as well.