Crowds of people walking through London under alien influence: Semi-check; the slaves in the parallel universe are technically under alien influence, though I'll agree it's pushing the definition.
Tie-in with Doctor Who story: Check; see last week.
Girl protagonist's mum is annoying: Check. She's more or less OK in the parallel universe, but it's business as usual when we get back home.
Mobile phone as plot device: Non-check-- well, it is the 1950s after all. Though, give the mobile addiction most of the characters in SJA seem to have, I'm surprised Rani and/or Clyde didn't whip theirs out right after arriving in the parallel universe to check if they've got a signal.
Luke says something so daft that you have to wonder how he gets through life without being mercilessly bullied: Non-check, though his mother gets in some daft lines about how wonderfully special it is to be in her gang.
Sonic lipstick: Check.
Wristwatch scanner: Check.
One or more of Sarah's companions falling under alien influence: Non-check-- in fact, it's a plot point that they're protected from it.