Heavy does in fact have a PhD, but he's never told his teammates. Initially he wanted to let them think he's just a dumb meathead to somehow troll them, but the joke's on him now because he thinks if he mentions it now, they'll laugh because they're so convinced he's just an idiot. So he'd have to punch them all in their little baby faces, and then cry a little on the inside. And he prefers to think that he's intentionally giving them the impression he's stupid than face up to the fact he really just doesn't come across very clever in English. But Medic just has a big ego about his own intelligence and thinks everyone is dumb, which is why he thinks he can get away with claiming that ribs grow back; he considers Heavy to be no dumber than any of the other dummkopfen he's got to heal and wouldn't be too surprised to find out that Heavy is smarter than he's been letting on. Meanwhile, Heavy hasn't told his dear old mama that he's a mercenary rather than a professor of Russian literature. She's old and doesn't need to know that her little boy gets shot, blown up, lit on fire, and axed in the face for a living. (Also, by the way, she knitted the Tough Guy's Toque and sent it to him in the mail.)
Also, if anyone else pulled that "hold your rib cage open for me" "CRUNCH" business on Heavy, he'd stick his hand down their throat to pull up their pants. Medic gets away with it. Wonder why...
Sniper has a twisted crush on Saxton Hale stemming from his own feelings of insecurity about his scrawniness and mustachelessness. He fantasizes about Saxton Hale fucking some proper Australianness into him.
Scout and Medic go jogging together every morning. It helps them both stay so speedy. Scout yaps away at Medic and when Medic is in a good mood he'll go, "mm-hmm, ja," etc. like he's actually listening. Scout used to insist on racing him, but Medic was always mildly irritated by Scout inevitably winning and being smug about it, so Scout stopped so he wouldn't drive him away and now jogs alongside him so he can yap at him.
Engie thinks Pyro is adorable. Even the enemy Pyro. That's why his domination lines for Pyros are so inoffensive and apologetic. They make s'mores over the burning bodies of Spies while they camp behind sentry nests, which is one reason why they're both a little chubby.
Medic has no prior experience with fighting. Neither does Engineer. It was a bit scary for them at first. At least Engie mostly avoids the front lines, but Medic doesn't, and he's really ferocious and scrappy to compensate for the fact he's a noob.
When cherub!Heavy suddenly trips and falls in Meet the Pyro, that's because the actual Heavy did the same thing, over a rock or a pothole or something. He's a little clumsy. Maybe it has to do with his fucked-up bodily proportions. Whenever Scout sees him fall over for no good reason, he yells "TIMBER!"
Medic always carries a spare pair of glasses. That's why Pyro steps on his glasses but when we see him he's wearing them. He's wearing his spare pair and the ones Pyro stepped on had been knocked off him somehow. He worries a lot about losing his spare pair, even though running around the battlefield half-blind and inevitably getting killed wouldn't be the end of the world, because it'd be embarrassing to get killed for a reason that doesn't apply to any of his teammates.
Demo sometimes drinks to the point of respawning. Also, one of the teams is cloned from the other, and he was the first to realize it, because they got more %$@?&%$@?&%$@?& than they've got the likes o' him, so what's another black Scottish cyclops, the same age, with the same appearance, in the same line of work, doing here? But nobody listens because he's kind of a paranoid conspiracy theorist. But most of his ideas are right. Such as that the war is kind of pointless and is never going to end.
Pyro is female, and around Scout's age. "Do you believe in magic, in a young girl's heart..."
Miss Pauling's previous job was in espionage.
Getting Pyrovision goggles and realizing why Pyros do their thing was a disturbing experience for the other classes. It's fun while you wear the goggles, but afterwards it keeps them up at night.