Roots: Lots of musical ones - You Are My Sunshine, Lucie refers to This is Spinal Tap ("let's take this up to eleven!") and Flash Gordon. Havers' role as a smooth-talking criminal recalls his starring role in The Charmer. Margaret the Vortisaur is probably named after Margaret Thatcher, as her predecessor Ramsay was named after a Conservative PM. The story features the song Bucimeana, adapted by Sutton from a traditional Hungarian poem set to the title music.
Double Entendres: "Let's get out there and do it!" "Next time I see him, I'll 'ave 'im!"
Technobbabble: The Doctor is able to get the TARDIS through the temporal current Zimmerman bled into the bulkhead doors. The Doctor has 'chronon nuclei'
Continuity: The Tar-Modowk live in the Vortex, feed on time and are drawn to it like flowers to sunlight. They are especially drawn to temporal anomalies (which they can 'smell'). They are roughly humanoid and much larger than humans (presumably taller rather than broader, unless the Doctor and Gordon ride side-saddle) and can be disorientetd by sonic vibrations. They ride saddled Vortisaurs through the Vortex. Time loops eventually erode the barriers between reality and the Vortex, allowing creatures like the Tar-Modowk and Vortisaurs through. The Tar-Modowk evolved from another species, Meg-bania and have spent aeons trying to find some trace of their previous existence: the time focus from the Meg-bania ship is the only surviving Meg-banian artefact. Vortisaurs have an excellent sense of smell and very acute hearing. Margaret is an especially large one, big enough for two humans. Temporal incursion appears to be preceded by bad weather.
Nick Zimmerman is humanoid, but not human, although he has the outward appearance of one. He is a thief of temporal technology, who then sells it on to the highest bidder. His time whip doesn't work on Lucie, because she isn't a full time sensitive (it paralyses the Doctor). The Headhunter abducts Lucie at the end of this story, causing the TARDIS Cloister Bell to ring and leading into Human Resources.
Lucie's Auntie Pat taught her a few things, including how to set up some really vicious feedback loops. Lucie used to 'hang out' with her a lot as a child.
The Doctor sends a sonic pulse through the TARDIS' outer shell to repel the vibration-sensitive Vortisaurs. There is a panel on the TARDIS console marked "Temporal Recurrence Warning", with a light that flashes if the TARDIS materialises inside a time-loop.
Q.v. 'Time Sensitivity'
Location: On board a Meg-bania timeship in the Vortex; inside Zimmerman's time loop [based on late twentieth-century Earth].
Unrecorded Adventures: The Doctor and Lucy have been dealing with Zimmerman for some time by the start of this story.
Links: The Doctor notes that he used to have a pet Vortisaur (Ramsey, who debuted in Storm Warning and remained in the TARDIS until Minuet in Hell). Lucie mentions her Auntie Pat (Horror of Glam Rock).
The Bottom Line: "Give Me Your Time!"
Part action, part runaround (Lucie's taking charge of the hunt for Zimmerman at the story's opening is a real surprise, part romantic tragedy, this is a weird beast and feels, not unlike the Doctor, Lucie and the Tar-Modowk, like something of a gate crashed party. As such it jars - there are some lovely performances here from the seasoned guests, but as a whole it doesn't quite add up. Perhaps if the first scenes were lost entirely it wouldn't have mattered?