I am a Dalek
Roots: There are references to Mary Poppins, the Womens' Institute, Jerusalem, Radio Two's Terry Wogan and Ken Bruce Shows, Anne Murray's "Snowbird", Brainteaser, Kennedy's assassination, John Lennon's "Imagine", Terry's All Gold, The X-Factor, Kylie Minogue, and Boots.
Goofs: Why does Kate being rubbish at maths mean she can't do sudokus? There is literally no maths involved at all in solving them.
I'm not sure how the geography works here. Crediton Vale is explicitly stated to be next to the sea and just a mile and a half from Winchelham. However it is clearly a short bus ride from Winchelham to Twyford, which is in Berkshire - nowhere near the sea.
Why are students having lectures at Durham University in the summer? The only part of summer when students are in attendance at British Universities is exam season, when there are very few lectures happening.
Continuity: Dalek casings are filled with booby-traps, making dead Daleks still dangerous; they can contain virus transmitters. Empty Dalek casings can run on automatic. At some point during the Time War (see Dalek), a single Dalek was sent back in time to Earth at the height of the Roman Empire to imprint the Dalek Factor in humanity [thus putting into execution the Emperor's plan from The Evil of the Daleks; everything about the Dalek here, including its ability to regenerate and self-repair damage, further suggests that the Daleks that fought the Time War are from the far future] and use their life force to create back-up from raw matter. The time capsule's engines malfunctioned, causing the Dalek to eject; it arrived on Earth but died shortly afterwards, but was able to release a small amount of the Dalek Factor, which was passed down through generations of humans to one in a billion including Kate Yates. When the dormant Dalek casing was disturbed by digging, the Dalek factor in Kate was triggered, drawing her to it and causing her Dalek life force to bring to life a new Dalek creature from data stored in the casing. The Dalek can use its sucker arm to grab and throw humans and cars about.
The Doctor knows how to remove a Dalek's gun. Whilst on the Moon, the Doctor carries a bag containing a string of flags of all the nations of Earth, as well as a flag bearing the crest of the Women's Institute. He also carries a bag of golf clubs. He can identify Frank's address as Redlands Road, Twyford, purely by the postcode. He has an old Time Ring in the TARDIS (Genesis of the Daleks). After the Dalek is destroyed, the Doctor wipes Kate's credit card debts, although he ruins her credit rating permanently in the process. He changes history by traveling back to 1970 and causing Frank to meet his wife several years early, so that he has more time to enjoy with her before he is exterminated.
There are spacesuits in the TARDIS with radio links built into the helmets (see The Moonbase, Four to Doomsday). The Doctor can turn off its gravity and change the pressure. The Doctor keeps a torch in a locker in the TARDIS. The Doctor turned off the TARDIS' emergency systems years ago, but at least one of them has switched itself back on.
Links: This story takes place at some point between New Earth and Army of Ghosts/Doomsday, and either before Mickey joins the TARDIS crew in School Reunion or after he leaves in Rise of the Cyberment/The Age of Steel.
The Evil of the Daleks (as well as the Dalek Factor, the Dalek uses the term "Flying pests" to describe birds), Dalek (Rose recognises the Dalek and the Doctor recalls killing them all in the Time War). There is a reference to Rose using the vortex to wipe out every Dalek in time and space in The Parting of the Ways. Rose recalls her father's death (Father's Day). The Doctor recalls meeting Nero (The Romans). The emergency systems are probably the HADS first seen in The Krotons. There are references to two different Dalek nicknames for the Doctor ("The Oncoming Storm" from The Parting of the Ways and the "Destroyer" from the novelisation of Remembrance of the Daleks).
Location: Winchelham, Crediton Vale, and Twyford, England, May [c. 2006]; Durham University, England, 1970.
Future History: The area of the Moon on which the TARDIS was trying to materialise isn't explored by humans until the forty-ninth century. The saying "Never turn your back on a dead Dalek" dates from the year 4000 (see The Daleks' Master Plan).
By 500,000,000AD, humans know nothing of Daleks or war; the Doctor describes it as "the most peaceful time in future history."
The Bottom Line: Short, sweet and rather charming, I Am a Dalek is written in the style of a Target Novelisation, and as such manages to be concise and effective at the same time. Kate works extremely well, the regulars are well-captured, and Roberts clearly has fun with the deadlier Daleks of the new series. Highly recommended.