Of all the "Meet the..." promotional shorts released so far, the Blu team has only been featured in the "Meet the Spy" promotional short. Even the sandvich in "Meet the Sandvich" belongs to the Red team, as can be deduced from the dialogue overheard.
According to webcomics created by Valve, the formation of the Red and Blu teams spawned over a land dispute between two brothers, Redmond and Blutarch, over plots of land bequethed to them by their deceased father, and has since persisted for over 100 years.
In the promotional video titled "Meet the Spy", there is a fight scene between a spy and a sniper where the spy slices the sniper's cheek. An update to the game was released that changed the sniper's in-game playermodel to include the scar from the video.
The game was first announced in 1998 as a sequel to first Team Fortress called Team Fortress: Brotherhood of Arms and early footage showed that the game was originally going to be a realistic military shooter game. But the game was changed over to be called Team Fortress: Invasion, and it would've featured the classes used in the game and a different team that was made up of aliens. The reason why the realistic military shooter was changed was because it was hard to tell the other classes apart.
As revealed throughout the TF2 comics, Scout's real name is Jeremy, and he was God's gift to Earth; Soldier is engaged to Heavy's sister Zhanna; Pyro has the psyche of a 3-year-old; Demoman's eye socket is haunted, his internal organs obey his will, and can change functions at his command (except for his liver, who seems to have a will of its own); Heavy's name is Mikhail and he has three sisters: Yanna, Zhanna and Bronislava; Engineer holds 11 PhDs and is the inventor of at least five life-extending machines; Medic's last name is Ludwig, he made a pact with the devil to bargain his soul out of hell, and he surgically added eight more souls to his self; Sniper's real name is Mun-dee, and he's the son of Bill-Bel and Lar-Nah of the lost civilization of New Zealand; Spy is Scout's dad, and he can seemingly disguise himself as anyone besides the nine mercenaries.
The Sniper's parents, Mr and Mrs Mundy, who appeared in the TF2 comics "Meet the Director" and "Blood in the water" were drawn in the likeness of John Patrick Lowrie (Sniper's voice actor), and Ellen McClain (the Administrator), who are actually husband and wife.
In issue #6 of the TF2 comics, the Medic explains to the Demoman that he has indeed fixed Demoman's eye several times in the past. Since the game was placed originally in 1968, and the Medic mentions eight occurrences of the incident, one per every Halloween, that places the game's story time close to 1976.
In the promotional short video "Expiration Date", Demoman is seen stepping onto a teleporter and disappearing from view for several seconds. He reappears moments later, wearing a Mexican sombrero and carrying a pack of beers, implying that the team has at least one teleporter exit placed somewhere in Mexico.