The Lazarus Experiment
Roots: Jekyll and Hyde, The Phantom of the Opera, the Star Trek: The Next Generation episode Genesis. The title and Professor Lazarus' name are both inspired by the Bible character of the same name. Both Lazarus and the Doctor quote TS Eliot's The Hollow Men.
Goofs: Martha knows that Tish has a job in PR. Then why is she so surprised that she's on the news? Especially when she's already got an invite to the event that Tish is talking about.
OK, let's talk about Lazarus's monster form. Firstly, none of the creatures whose features are seen in Lazarus's monster form (insects, crustaceans, and scorpions) are supposed to have been part of the evolutionary lineage of human beings. Secondly, these features shouldn't work for a human-sized being in Earth's atmosphere gravity. Lazarus's exoskeleton should shatter when he runs.
There is no way that the gas taps the Doctor opens would produce enough gas for an explosion in the time available.
Not technically a goof, but it's odd that Tish needs to explain that she knows that the church is Southwark Cathedral because Lazarus told her.
The sounds made by the pipe organ bear no relation to the notes that the Doctor was actually playing.
The way that Lazarus turns back to his old-aged self after he dies is somewhat weird. Especially as it happens whilst the Doctor is closing his eyes. I could accept it happening at the instant of death or as a gradual change starting straight after death, but happening within the space of a second or two starting at least a minute after death really jars.
Technobabble: The Doctor describes Lazarus' equipment as "a sonic micro-field manipulator" and "using hypersonic sound waves to create a state of resonance."
Using hypersonic soundwaves to destablise the cell structure, then a metegenic program to manipulate the coding in the protein strands apparently means hacking into his own genes and instructing them to regenerate.
Dialogue Triumphs: Professor Lazarus: "That's an interesting perfume. What's it called?"
Continuity: Martha's sister Tish is head of the PR department for Professor Lazarus' organisation. She is clearly uncomfortable with Lazarus's attempts to flirt with her until he rejuvenates himself, after which she starts flirting with him. She also has a good enough memory to be certain that the Doctor isn't on the guest list. Tish implies that Martha doesn't have much of a social life.
Lazarus has invented a process that enables a human being to return to a much younger body. The process causes an energy deficit, making the person who uses it hungry. However, afterwards he continues to mutate, ultimately turning into a monstrous creature, because he activated something in his DNA that won't let him stabilise.
The Doctor wears a Tuxedo. The sonic screwdriver can track energy signals. He says that a long life leads to you being tired of everything and left alone. In a deleted scene, he thinks he's lost the first draft of the US Declaration of Independence until he finds it in his tuxedo pocket.
Links: Martha mentions seeing Shakespeare (The Shakespeare Code), New New York (Gridlock), and Old New York (Daleks in Manhattan/Evolution of the Daleks). Mr Saxon is funding Professor Lazarus's experiements. The Doctor says that whenever he wears his tuxedo something bad always happens (Rise of the Cyberment/Army of Ghosts, and presumably several unrecorded adventures). The Doctor claims that he has some experience with this kind of transformation (a reference to regeneration). The Doctor mentions being in the Blitz (Illegal Alien; Just War; The Empty Child/The Doctor Dances)
Extras: This story has an episode of Doctor Who Confidential. The BBC website had an online commentary, which has since been taken down. It also has a behind the scenes video podcast.
Location: Martha's flat; Lazarus Laboratories; Southwark Cathedral. It's the day after Smith and Jones.
Unrecorded Adventures: The Doctor claims that he hung around with Beethoven. In a deleted scene, the Doctor finds the first draft of the US Declaration of Independence before he got them to put in the bit about the pursuit of happiness and says that Thomas Jefferson was funny. He spoke Gaelic and was very keen on tomatoes.
Q.v. Mister Saxon, The Sound of Drums
The Bottom Line: 'I'm old enough to know that a longer life isn't always a better one.' At first glance, it seems like a fairly formulaic runaround which comes to a natural end fifteen minutes before the end. But look deeper, and there's actually quite a bit of thematic depth - especially in the fifteen minute "coda" - with an exploration of the meaning of mortality and our attitudes to death. It's still not a classic, but it is fairly substantial.