Crowds of People Under Alien Influence: Non-crowds of people, removed due to alien influence. Sort of a bizarro-universe crowd.
Tie-in with Doctor Who story: No out-and-out tie-in, but a lot of referencing: Turlough (alien prince hidden on the Earth), The Android Invasion (mysteriously deserted English urban conurbation), the Judoon, The Daleks' Master Plan episode 12 (returning to a planet to find it deserted), The Curse of Fenric (Clive's "I love you, Mum!" when finding himself trapped); plus a reference to "Survivors" when Rani says "Please don't let me be the only one."
Rani's Mum is Annoying/Is Absent: The latter, though that's no different to anyone else. And she does get a good panic at Rani's Dad over the phone when they think Rani is missing.
Luke/K9 Cameo: None, though Clyde and Rani spend a lot of time wishing there was one.
Sarah Jane Waxes Maudlin: Episode Two ends with a heroic maudlin-fest as Sarah Jane, Rani and Clyde gush about how great it is that they know each other.
Mobile Phone as Plot Device: Is back, hooray!
Racism Towards Aliens: When Clyde considers the possibility that Gavin might be an alien, he leaps straight away to the conclusion that Gavin somehow caused the disappearances. Although everyone can be forgiven for assuming initially that the great big Cyberman/NuDalek-offspring robots are up to no good.
The Crimes of Sarah Jane: Well, Sarah Jane is absent this story, but Clyde and Rani severally engage in: Breaking and entering (Rani, Gavin's flat), use of private property without permission (Clyde in the cafe-- it's not theft, as he leaves money to pay for it), and Grand Theft Bicycle ("we'll bring them back," Rani says, though there's no evidence that they do).
Sonic Lipstick: Rani grabs it and uses it repeatedly, in some kind of symbolic female rite of passage.
Wristwatch Scanner: Was presumably on Sarah Jane's wrist when she vanished, so Rani doesn't get that too.
One or More of Sarah's Companions Falling Under Alien Influence: Retroactively-- Clyde and Rani being grounded by the Judoon means they don't get Raptured along with everyone else.
Sarah And/Or Companion Acts like a Selfish Cow: To be fair to them, no more than anyone else would in similar circumstances.