You can always judge a man by the quality of his enemies.
—The Doctor
Written by Ben Aaronovitch, who went on to write the Rivers Of London series.Despite being aired in the show's 25th anniversary year and featuring many links to Doctor Who's very first serial, "An Unearthly Child", this is not the official 25th anniversary special. That was "Silver Nemesis", the first episode of which aired on the actual anniversary.The Doctor and Ace arrive at Coal Hill School, perhaps a month after the First Doctor and company left. It doesn't take long before they're mixed up in trouble of the Dalek kind — two separate Dalek factions, the Renegades (Grey) and Imperials (White), respectively opposed and loyal to Davros (as seen in "Revelation of the Daleks"), wage war on each other for possession of the Hand of Omega, a Time Lord superweapon. And unfortunately for both groups, the Doctor has laid a trap for them; he just has to make the right conditions to spring it and ensure that Group Captain Gilmore and his men don't get diced in the crossfire.
Tropes
Arson, Murder, and Jaywalking: Used by the Doctor to mock Davros: "Crush the lesser races! Conquer the galaxy! Unimaginable power! Unlimited rice pudding! Et cetera! Et cetera!"
Deliberate Values Dissonance on that one. His racism was pretty much acceptable public opinion (or at least not far off) at the time.
He's still bad even in the Values Dissonance context. Even back then people didn't cohort with Nazis and Daleks and carry a Platinum Master Race Card. His fellow servicemen, presumably a bit Values Dissonance themselves, weren't very impressed with him after they found out, to say the least.
Attack Its Weak Point: The Doctor mentions that the Daleks are weakest in the eyepiece. So that's where Ace shoots one of them. With a rocket launcher.
Without wanting to diminish the awesomeness of the moment in question, it should be noted that the Battering Up is done with a baseball bat that has been super-charged by an alien super-weapon to make it a more or less fair fight.
Bavarian Fire Drill: The Doctor just waltzes in to Rachel's van and starts asking a lot of technical questions, and at first she doesn't bat an eye. It takes her about a minute to start cottoning on and asking just who he is.
Ace's anti-tank missile might be a less extreme example
Briar Patching: How the Doctor makes the Daleks lose hardest of all.
Breaking the Fourth Wall: You know the quote under the picture at the top? Said by the 7th Doctor to the audience at the end of part three.
Broken Pedestal: Mike Smith comes to realize that Ratcliffe isn't the untarnished, infallible hero he saw him as.
Ace, in turn, is left feeling pretty betrayed by Mike when she realizes that he's not quite as heroic as she'd built him up to be. That, and he's a Nazi.
Casting Gag: Michael Sheard, who plays the Dalek-controlled school headmaster, also played Mr. Bronson, the mean-spirited Latin teacher at Grange Hill.
Cold Open: A zoom out on Earth, with the Dalek mothership entering shot above the camera.
Continuity Nod: Mostly with sets such as the Foreman junkyard and Ian's classroom at the Coal Hill School (which still has the book on the French Revolution that Barbara gave Susan in it).
Five, six, seven, eight It's the doctor at the gate...
Darker and Edgier: Of a sort; from this story on, the Seventh Doctor begins to be presented as a darker, more brooding and manipulative character than the amiable prat-falling metaphor-mixing bumbler of the previous season.
Evil Is Hammy: Davros has completely lost his shit in this one.
Exact Words: In their confrontation, the Doctor tells Davros not to use the Hand of Omega, that it's something that's not to be trifled with, and that he's making a grave mistake in doing so — all of which is true, but he doesn't mention why.
Fantastic Racism: The Daleks are in the story, so that's a given. But here we see for the first time just how fanatical they can get: they declared all out civil war just because the Imperial Daleks are a tiny bit different genetically. This is an Ironic Echo to the all-too-real racism present in 1963.
Foreshadowing: An unintentional variant from the Seventh Doctor in Part 2 concerning defeating the Daleks: "I mean, what do you expect to do, talk to them sternly?"
Five Rounds Rapid: Played straight early on, then subverted when the military gets better weapons.
Grand Finale: To the Doctor vs the Daleks story arc for the Original Series.
Guile Hero: This episode is the first real showing of the Seventh Doctor's manipulative side.
Go for the Eye: Ace + rocket launcher + this trope = Epic Win.
Harsher in Hindsight: The little girl is released from the Daleks' mind control! But a later short story shows that she was driven irreversibly mad by the experience.
The Renegades aren't much better. When the two factions are lined up across from one another and firing, there is one Imperial casualty to the zero Renegade ones.
I Never Said It Was Poison: The mole gives himself away by asking the Doctor an honestly-curious question about the Daleks that reveals he already knows something about them that the Doctor never told him.
Ironic Nickname / Non-Indicative Name: Group Captain "Chunky" Gillmore, who's 6'4" and looks like he weighs about 110 pounds. However, on the DVD Commentary, Sylvester McCoy revealed that it came from Gilmore's nickname for his revolver (owing to its "chunky" shape), and the name stuck.
Mythology Gag: The telly is cut off before it can announce the new show that is premiering that's called Doc-.
No Swastikas: Ratcliffe and his groupies are hinted to be a miniature Hitler Youth, though they could just as easily represent the National Front or some other nativist movement.
Non-Indicative Name: The Hand of Omega looks nothing like a hand. The Doctor claims the name came about due to the Time Lords' "infinite capacity for pretention".
Oh Crap: The Doctor's expression when, having escaped from a Dalek up a flight of stairs, he hears it powering up its antigravs.
Pin-Pulling Teeth: In a possible allusion to this trope, the Doctor pops the cap off one of Ace's nitro-nine cannisters with his teeth.
Politically Correct History: Averted, for one of the few times in the history of Doctor Who. Most noticeably with Ace discovering a "no coloureds allowed" sign. Mike Smith also makes reference to "[keeping] the outsiders out"note Ace has perhaps the most Backstory of any of the Classic companions. For one, as a child her friend Manisha's flat was firebombed by skinheads, so naturally she's less than pleased by both the sign and Mike's words.
Not only that, but the black cafe worker who serves the Doctor notes that the existence of sugar is the reason why his grandfather was kidnapped from Africa to become a slave, and his family subsequently became English.
Rebuilt Set: The entrance to Foreman's Yard, as seen in "An Unearthly Child" (when it was a set) is recreated on location. Unfortunately "Foreman" is misspelt as "Forman".
The Reveal: Two successive audience-teasing ones: first when it's revealed that the Renegade Daleks' battle computer isn't Davros, which most people were assuming when the show was first broadcast, and then when it's revealed that the Imperial Dalek Emperor is.
Skip of Innocence: The little girl skips around town when she's not plugged into the Dalek battle computer. She's not exactly "innocent", though.
Smug Snake: Ratcliffe spends most of the story strutting around acting like a little tinpot general. When the Renegade Daleks get the Hand of Omega and no longer need his services, however, it quickly becomes apparent that he's completely out of his depth.
Star Killing: The Hand of Omega is designed to do this, to provide the massive power source required for time travel. The Doctor uses it to destroy the solar system where the main Dalek force is located, to prevent the Daleks using it on anyone else.
Talking the Monster to Death: The Doctor tells the last of the Renegade Daleks that it's got no kin left at all since its home world was blown up. It refuses to believe him at first but, unable to contact anyone, is brought to so much despair that it disintegrates itself.
Tele Frag: The Doctor manages to make this happen to a Dalek on itself, by fiddling with the machine so that half of the Dalek materializes where the other half would be.
There Is No Kill Like Overkill: The Abomination Special Weapons Dalek. When the white Daleks can't gain the upper hand, they wheel out this thing. No plunger, no egg whisk, no eyestalk — just a single massive cannon. When it opens up on the grey Daleks, there's nothing left except little patches of smouldering ash.
Xanatos Speed Chess: The first episode to properly show off the Seventh Doctor's manipulative side. Unforseen events do crop up, but they don't seem to slow him down any.
X-Ray Sparks: the Dalek extermination effect used in this story was so cool and memorable that it was revived almost twenty years later, despite only appearing this once.
You Have Outlived Your Usefulness: The Renegade Daleks do this to Ratcliffe's organisation, and are about to do it to Ratcliffe and Mike when the Imperial Daleks attack.