Smith and Jones
Roots: The Judoon appear to be a cross between Sontarans, the Ohnir from Trading Futures and the Vogons The Hitch Hiker's Guide to the Galaxy. The idea of a story set in a building that's been transported to the moon is lifted from Timewyrm: Revelation. Mr Stoker is clearly named after Bram Stoker, the author of Dracula. Martha mentions The Navigator.
Goofs: Why is Mr Stoker called Mr rather than Dr? In UK hospitals, only surgeons go by the title Mr, and yet Stoker is clearly depicted as a non-surgical consultant.
The scene in the X-Ray room appears to break a number of laws of Physics. Firstly, where does the power come from to increase the radiation by 5000%? [Perhaps it's from the sonic screwdriver's power supply.] Secondly, the Doctor absorbing all the radiation and expelling it into his show without damaging the shoe or making it dangerously radioactive is rather implausible. [It could possibly have been done with nanites, but even then, you'd expect some damage to the shoe.]
Speaking of radiation, the Doctor's immunity to it is somewhat at odds with numerous stories, most memorably The Daleks, Planet of the Spiders, and Destiny of the Daleks. Yes, it's a different form of radiation, but it still jars.
The Plasmavore turning the MRI scanner into a weapon doesn't work very well. Firstly, a magnetic pulse might disrupt electronic devices, but it shouldn't kill a person. And a strength of 50,000 Tesla would have no noticeable effect at a distance of 250,000 miles. It certainly wouldn't kill half the Earth's population.
Why doesn't the blood loss cause the Doctor to die or regenerate? [This could be something to do with his second heart, except that he's been in danger of dying through blood loss before, in The Eight Doctors]
The Royal Hope Hospital is practically next to the spot the ship crashed in Aliens of London, and yet that story claimed that the nearest hospital was actually the Albion hospital.
Continuity: Martha Jones is a medical student, currently training at the Royal Hope Hospital. She has a brother called Leo, who is having a 21st birthday party, and a sister called Tish. Leo appears to have a baby [the script says that the baby is six months old]. Her parents have split up, and her dad is now in a relationship with a woman called Annelise.
The Doctor says he doesn't have a brother any more. [Perhaps a reference to Irving Braxiatel?]. He recognises the Judoon from a distance [presumably from the design of their spaceships]. He can use the sonic screwdriver to increase the radiation from an X-Ray machine by 5000%, although that screwdriver is destroyed in the process. He isn't harmed by the radiation, as it's only Roentgen radiation, and he used to play with Roentgen bricks in the nursery. He can also expel the radiation from his body into his shoes, which are then harmless enough to casually drop into a bin. [See goofs]. When the plasmavore drinks his blood, the Doctor appears to be dead to the Judoon scans, but is revived when Martha performs CPR on him [although this may be co-incidental]. He says that crossing into established events is strictly forbidden, except for cheap tricks.
The Judoon have a translation device that can identify a language based on a few words and enable them to speak it, and a device that can quickly scan an individual's species. They are police for hire, more like interplanetary thugs. Galactic law means they have no jurisdiction over the Earth. They have access to H2O scoops, enabling them to take the hospital to the moon. It relies on plasma coils. It isn't made clear whether the Judoon are a species or an organisation.
Slabs are solid leather all the way through, and are basic slave drones. They always travel in pairs.
The Plasmavore is a shape-changer, able to change her internal shape to fool the Judoon instruments into thinking that she is a human. But she needs to drink a person's blood in order to do so.
Links: Martha mentions events of the last few years including the spaceship flying into Big Ben (Aliens of London, "Christmas" (presumably The Christmas Invasion, and "those Cybermen things" (Army of Ghosts/Doomsday). She also mentions her cousin Adeola, who worked at Canary Wharf (Army of Ghosts). The Doctor mentions liking a little shop in a hospital (New Earth). There is brief mention of Mr Saxon (The Runaway Bride), who says that there is life out there, and we see a "vote Saxon" poster. The Doctor mentions Rose, saying that she was a "recent" occupant of the TARDIS. The Doctor mentions several TARDIS components, including the gravitic anomaliser, the helmic regulator, and the handbrake.
Extras: This story has an episode of Doctor Who Confidential. The BBC website had an online commentary, which is no longer up.. It also has a behind the scenes video podcast.
Location: Central London and the moon. [Presumably it's 2007.]
Unrecorded Adventures: The Doctor mentions meeting Benjamin Franklin when he discovered that lightning is a form of static electricity. He got rope burns off the kite, got soaked, and then got electrocuted. He claims that he did have a laser spanner, but that it was stolen by Emmeline Pankhurst.
Q.v. Mister Saxon, The Sound of Drums
The Bottom Line: "We're on the bloody moon." Plotwise, Smith and Jones is just a standard runaround. However, the whole point of the story is to introduce Martha, and it succeeds fantastically. Martha is immediately more likeable than Rose, and shows great promise as a companion. The Plasmavore, the Slabs, and the Judoon are all fantastic and memorable new aliens, all well worth revisiting. Not the best Doctor Who story ever, but it does the job with some degree of style.