Crowds of people walking through London under alien influence: No, though there's crowds of plant spores floating through London under alien influence. Also, crowds of people being driven through London in ambulances under alien influence.
Tie-in with Doctor Who story: Distantly, as it's part of the cycle of Slitheen-featuring stories taking over the Sarah Jane microverse like a stand of rackweed. There's also an oblique "Children of Earth" reference in Sarah Jane's line "My son is dying just to feed your addiction."
Rani's Mum is annoying: Rani's mum is absent. So is Rani's Dad, at a convenient "headteacher's conference," or are they trying to rebuild their shattered relationship?
Star Wars reference: No.
Mobile phone as plot device: Yes, along with every other electronic device in London.
Luke says something so daft that you have to wonder how he gets through life without being mercilessly bullied: No, mainly because he spends most of the story unconscious and thus unable to do so.
K9 interprets a figurative English expression literally: Sort of-- his overgeneral interpretation of "test" as being a way that one human proves intellectual superiority over another means that Clyde can talk him into helping him cheat (on the grounds that figuring out a way to do so is also a means of proving intellectual superiority).
Sonic lipstick: Check, and yet again as a sophisticated lock-pick cum offensive weapon.
Wristwatch scanner: Check, and it's a serious plot device as Sarah Jane's scan of the Blathereen's teleport coordinates enables her to track them down.
One or more of Sarah's companions falling under alien influence: Luke, for most of the story.
Sarah and/or companions acts like a selfish cow: Clyde's attempt to cheat on exams using K9 (how the hell did he reckon this one would go unnoticed?).
And, because it's the last episode of the season:
Wide-eyed speech by Sarah Jane about the wonders of the universe and how great it is to be in her gang: Check, also including quick arse-covering section to the effect that not all aliens are evil, just in case they get accused of racism for their constant portrayal of non-humans as criminals, idiots and/or chavs.
Next year, I'm going to include "Somebody says 'maximum [something]'" in this checklist, because I reckon it happened at least once per serial this year.
Also: Simon Callow appeared in this?!