Shrug of God: Marc Laidlaw is very ambiguous about some parts of the overall continuity. Not only towards the things added on by the Gearbox expansions, but also when it comes to Valve's own games.
The whole issue of canon is something the fans came up with. I guess you will be able to identify as canon those story elements we continue to build on and develop and mention repeatedly as the story progresses. Others might fall by the wayside once they've served their purpose. Couldn't you say the same of us all?
Throw It In: It's fair to say that a good amount of the games came about by accident.
In playtesting for Episode One, Dog's idle animation had a shake of his head that happened to line up with the point where Alyx ensured he had done the calculations when proposing to throw them into the Citadel. Testers found it hilarious, and it was preserved through development of the scene.
Similarly, in the level "Freeman Pontifex", there is a bit where a fast zombie is hiding in a dumpster. But when you throw a grenade, it throws it back. The lobbing back of the grenade was originally unintended; it happened because the script that was supposed to make the boxes explode out of the dumpster as the zombie got up would trigger and sometimes hit the grenade back to Gordon. Of course, it was too good to leave out.
The vista of the Nectarium in Episode 2 came about when a dev was making space for the mine cart trap and knocked out a wall, which conveniently opened up a vista of the Nectarium. All this elegantly lined up with Valve's design philosophy of letting the player see their goal, even before they realize it is their goal, making for a happy accident.
The Hunter-Chopper's minespam tactic was a glitch at first - the chopper dropped so many mines at once it destabilized the game. However, the programmers liked it, so they toned it down to a more reasonable amount and added it to the game as a Desperation Attack.
Gunships' original behavior caused them to focus on the "biggest threat". They weren't originally supposed to attack fired rockets if you kept the laser sight on them, but they did, because as soon as one was launched into the air, the rocket itself became a significantly more deadly threat than Freeman himself. So they kept the behaviour in for extra challenge.
Vaporware: Common with this series (and even more so for Team Fortress 2, though it did finally get released). Fans have been waiting for Half-Life 2: Episode Three for so long that it's become a source of videogame-culture running gags, and every bit of Valve-related news will include comments like "But what about Episode 3?" and "Wait: [a convoluted chain of "logic" like a parody of a conspiracy theory]...HALF LIFE 3 CONFIRMED!"
To put it in numbers: 2 was released in 2004, almost exactly six years after the original in 1998. Episode One had a much quicker turnaround, taking only two years to get a 2006 release. Episode Two miraculously managed to come out only a year after, in 2007. As of August 2014, Episode Three is still unaccounted for, and is quickly closing in at seven years and counting since Episode Two's release.