The Girl in the Fireplace
Roots: Clockwork robots are a mainstay of the Steampunk genre. Similar beings have previously appeared in Doctor Who in Death and Diplomacy, The Clockwise Man, and The Resurrection Casket. Rose mentions Camilla [Parker-Bowles]. The Doctor sings "I could have danced all night". The differences between time in France and on the ship might have been inspired by a similarly strange correlation between time passing either side of a magic door in CS Lewis's Narnia books. The scene where the Doctor briefly plays Reinette's harp is a nod to The Five Doctors. The Star Trek: Deep Space Nine episode "The Visitor". The "magic door" explanation is similar to how the Cat describes a passage into the past in the Red Dwarf episode "Stasis Leak". It may also be a reaction against science fiction shows that overuse technobabble. The rotating fireplace is similar to the rotating dresser in 60s show Batgirl, though the idea probably goes back much further.
Goofs: The behaviour of the fireplace window is quite strange. When the Doctor is talking to Reinette through the fireplace, the time in France and on the spaceship is synchronised, as it is when he is on the French side of it. However, when he's on the ship side and not talking to Reinette, time flows much faster (and at a variable rate) on the French side. Interestingly, we never see any hint of this effect with the other time windows - Reinette doesn't seem to go missing when she walks through to the spaceship.
At the end of School Reunion, Rose hated the idea of Mickey being aboard the TARDIS. Here, she seems fine with the idea of him coming along, and not much time has passed in-between, as Mickey says that it's his first trip.
Why doesn't the TARDIS translate Reinette saying "Monsieur"?
Reinette says she was seven when she met the Doctor as a child, and yet she also says that it is 1727. However, she was actually born on the 29th of December 1721, so she's actually five, or possibly six.
How do the clockwork robots wire human body parts into machinery? The two examples we see have no biological systems to maintain the body parts in working condition.
As Mickey asks, just what is the horse doing on the spaceship? Did it just happen to walk through one of the time windows (and, if so, why was that window left wide open for anything to walk through) and avoid being taken apart for parts by the robots, or was it already on the ship and somehow avoided being taken apart for the year since the ship was stranded? Either way, it didn't show up when the Doctor scanned for lifeforms.
Why doesn't the service robots' programming prevent them from using the crew for parts?
There are several scenes where the robots put their dissection tools next to a human's body, yet we never see them even attempt to use them.
Why, exactly, does being part of events mean that the Doctor can't use the TARDIS to get to France? He's used it to travel around within an adventure before - as long as he doesn't arrive before he left, he isn't breaking any kind of causality. And why - at the end - doesn't he return to pick up Reinette by using the TARDIS instead of using the fireplace? [It has been suggested that the nature of the time windows would make such a trip either very difficult or impossible. Though this raises the question of why the Doctor claims that it's because he's already involved in events.]
If, as the Doctor says, the fireplace window is offline when the robots attack the party then how does the audio link clearly pick up Reinette's words shouted through the fireplace, which is nowhere near the window? Especially as there is no background noise of party goers screaming in this scene.
Technobabble: The Doctor makes up the term spatio-temporal hyperlink as an alternative to "magic door". He uses multi-grade anti-oil, which looks like red wine, and shuts down [almost] any mechanical system.
Dialogue Disasters: The Doctor: "You're Mr thick thick thickety thickface from thicktown thickania. And so's your dad."
The Doctor to a clockwork robot: "I'm not winding you up." Groan.
Dialogue Triumphs: Rose: "We're in deep space. They didn't just nip out for a quick fag."
The Doctor: "Yep. Checked all the smoking pods."
Mickey: "What's a horse doing on a spaceship?"
The Doctor: "Mickey. What's pre-revolutionary France doing on a spaceship? Get a little perspective."
The Doctor: "France. It's a different planet."
Rose: "You're not keeping the horse."
The Doctor: "Why not? I let you keep Mickey."
Reinette: "There is a vessel in your world where the days of my life are pressed together like the chapters of a book so that he may step from one to the other without increase of age whilst I, weary traveller, must always take the slower path."
Reinette: "The monsters and the Doctor, you cannot have one without the other."
Reinette: "One may tolerate a world of demons for the sake of an angel."
Reinette: "This is my lover, the King of France."
The Doctor: "Yeah? Well I'm the Lord of Time."
Continuity: 51st Century Warp engines are capable of punching a hole in the universe.
The Doctor can tell that Reinette is speaking 18th Century French [either this is despite the TARDIS's translation or because he genuinely speaks French and it isn't being translated for him. Incidentally we also see this in Shadowmind]. Reinette is able to read his mind when he tries something like a mind meld with her. She discovers that he is lonely, and has been since "being a boy", and that he knows the name of every star. He acts drunk to fool the robots. He refers to himself as "the lord of time" [presumably as he's the last Time Lord].
The service robots on board the SS Madame de Pompadour are made of clockwork, and can be stopped by the fire extinguishers aboard the ship [possibly they freeze the parts]. They have short-range teleports which can travel through the time windows, though only when close to them. They are capable of wiring human body parts into the machinery. The ship should have had a crew of over 50 people. [The Tardisode establishes that the ship was originally damaged by an ion storm, which would disable all electrical devices - presumably the clockwork service robots are designed to operate under such conditions.]
Mickey panics when he and Rose are captured by the robots. This is his first trip in the TARDIS and it is implied that he hasn't seen beyond the console room.
The Doctor claims that being part of events means that he cannot use the TARDIS to take him, Mickey, and Rose to Reinette's time.
The sonic screwdriver is capable of detecting that the fireplace is a genuine 18th Century fireplace, and of drawing the robot out from under Reinette's bed, and is capable of repairing a loose connection in the circuitry of the time window.
Links: Mickey joined the TARDIS in School Reunion, and this is explicitly said to be his first trip. Mickey also mentions Sarah-Jane Smith (School Reunion). The Doctor says that monsters have nightmares about him (Love and War). Rose mentions the Doctor being the Oncoming Storm (The Parting of the Ways). Zeus plugs were first mentioned in The Hand of Fear.
Extras: This story has an episode of Doctor Who Confidential. The BBC created a one-minute trailer called a "Tardisode" for each episode of series two, which was available to download on your mobile or watch at the BBC website. They also made a commentary track available online. Neither are still up.
Location: Paris in 1727, 1745, 1754, 1759, and 1764, as well as possibly an unstated date between 1727 and 1745. The SS Madame de Pompadour in the Diagmark Cluster, two and a half galaxies from Earth in the 51st century, though a caption says that it is 3,000 years after 1759 (i.e. 4759).
Unrecorded Adventures: Mickey says that the Doctor mentioned Cleopatra and called her Cleo, and Rose says he only did so once.
The Bottom Line: 'A spaceship from the 51st Century stalking a woman from the 18th.' Although there are several galaxy-sized holes in the plot, this works really well. The design is fantastic, but the key aspect is the brilliant performances of David Tennant and Sophia Myles and the emotional intensity of their relationship.