All for Nothing: Most episodes' "A"-plots end like this, with something the team has been working hard to get right ultimately being scrapped.
All Love Is Unrequited: The fact that Sally is obviously head-over-heels in love with Ian is an elephant that remains strenuously ignored by everyone in the room. He starts out entirely oblivious, but increasing hints that he's noticed the UST emerge late in the series.
Artistic License - Geography: In-universe, Graham Hitchens' answer to the problem of ensuring that the Olympic torch relay will pass within a certain distance of 90% of the population is to redraw the map so that the major cities are closer together.
As Himself: Lord Coe. And in the last episode, Aled Jones.
Berserk Button: Kay Hope is Head of Sustainability. DO NOT suggest she has anything to do with Legacy.
In the second episode, Kay angrily corrects the interpreter who calls her "Head of Legacy" in Portuguese.
Big Eater: Head of Infrastructure Graham Hitchens is constantly seen surrounded by and/or eating copious amounts of outrageously-flavoured junk food.
Life Imitates Art: Given that there's a large-but-finite number of things an Olympic Organising Committee have to organise, and the show's whole premise was that all of them would cause problems, it was inevitable that they'd be on target with a few of them. The problems with the countdown clock were particularly prescient.
Of Course I Smoke: Kay pulls this when she realises that Ian and Fi's smoke break allows them to have conversations that she's not part of.
Only Sane Man: Ian Fletcher thinks he is, and part of the conceit of the show is that he's presented as if he is. There isn't really one at all, though bluntly-spoken Yorkshireman Nick Jowett usually comes the closest.
Refuge in Audacity: Ian, quite often, in conjunction with I Meant to Do That, e.g. conjuring up some convoluted artistic media statement to explain away the fact that, due to an almighty cock-up by Siobhan, the Olympic countdown clock actually counts up.
The Rival: Once the office gets a new employee in charge of Legacy on top of the one in charge of Sustainability, the claws come out, since Kay was already annoyed that nobody could tell the difference.
Rouge Angles of Satin: Ian is alarmed to see that the website is riddled with spelling errors only a day before its launch.
Ian: This, though, it's just a little thing, but this... "Olypmic"? Is that some kind of, uh..? Barney: Oh yeah, that, you know, that's just, like, spelling. [beat] We can change that any time. [beat. Ian gives him a prompting look] I mean do you want me to- Ian:[cheerfully] Well, why not? Barney:[hesitantly changes it to "Olypicm"] There. That better? Ian: Well it's different.
Running Gag: Ian's difficulties with the card-entry doors and inability to fold his folding bike without injuring himself.
Sixth Ranger: Fi Healey, head of Legacy. Most of the office take to her immediately, but Kay is annoyed at the confusion absolutely everyone shares between Legacy and Sustainability, and Fi's greater popularity just makes her dislike her even more. Sally also seems (quietly) worried about her flirting with Ian. Also a Sitcom Arch-Nemesis.
Spanner in the Works: Ian Fletcher's best-laid plans are constantly broken by politically correct red tape, causing him to resort to smoking very early on in the series.
Trailers Always Spoil: Lord Coe's appearance at the end of episode two was clearly meant to be a surprise, but it seems nobody thought to tell the publicity people to keep it secret, so it was mentioned in just about every pre-transmission article about the show as well as in the trailers.