Roots: The so-called 'Philadelphia Experiment' and its main detractor Carlos Allende. The Doctor also name-checks Morris K Jessop's book The Case for the UFO. The Doctor refers to the 'Butterfly Effect' originally coined by Edward Lorenz and Einstein's Unified Field Theory. Professor Tessler's name may be a nod to Nicola Tesla (who purportedly devised his own unified field theory shortly before his death). Peri attempts to whistle The Yellow Rose of Texas and 'sings' Row, Row, Row Your Boat. Hamlet and Snow White (implied patricide/regicide, a wicked stepmother) Laurel and Hardy ("another fine mess you've got us into"). Churchill's 'their finest hour' speech.
Double Entendres: "Doctor, I'm finding it hard to swallow"
Continuity: The TARDIS has become trapped in an inter-dimensional flux, the point of connection between two dimensions. Previously it was en route to Baltimore so that Peri could reassure her family of her safety, having not seen them since Lanzarote (see: Links). 'Macro' universes are divergent dimensions created by alternative timelines. As such timelines are infinitely generating with each passing action, the Universe accommodates their respective 'space' by reducing their relative size - it could therefore be inferred that Kapron's universe is not only microscopic, but younger than ours.
Invisibility experiments involving the USS Eldridge have also put the ship in the area of flux, trapping it in a loop of slow decay for sixty years. The vessel is gradually succumbing to a green rust, while most of its surviving crew are trapped in the causal loop, with those unaffected also trapped, but neither subject to the time loop nor aging.
Kapron is a militaristic planet in a macro-dimensional universe. Its technology is apparently far in advance of Earth's (or Earth's of the 1940s), nevertheless horse and carts are still in use. The arrival of the TARDIS has allowed the time ship's and the Eldridge's power sources to leach into Kapron's dimension, resulting in a vividly glowing atmosphere (the Doctor likens it to the Aurora Borealis) and a ready supply of energy which the Kaprons 'mine' through condensers and spend on their ruler Osloo's war efforts.
Travelling between the macro universe and the normal one requires re-setting the TARDIS' dimensional stabilisers, lest anyone exiting the Ship be aged or made younger by the effect of dimensional change. The Doctor is able to reverse the aging effects on Peri through the use of the TARDIS' zero room (see: Links)
Peri can't sing, and knows what a capstone is.
The Doctor intended to pilot the TARDIS to Baltimore, enabling Peri to tell her family she is alive and well after her time in Lanzarote (see: Links) He has a battery he pocketed while in 'Foxy's lab, which contains enough power to fuel Kapron's universe for millennia. He uses the alias of John Smith. Once again he avows that he doesn't believe in ghosts.
Links: Along with her time on Lanzarote (Planet of Fire) Peri recalls the events of Vengeance on Varos (her transmogrification), The Two Doctors (Androgums), Mission to Magnus (Ice Warriors) Hollows of Time (Tractators) and Point of Entry (the astral plane). The Doctor makes reference to 'Foxy' Foxwell (Hollows of Time). The 'time rust' affecting the Eldridge may be connected to the temporal corrosion seen in The Girl Who Never Was. Castrovalva (the TARDIS' zero room) Peri and the Doctor eventually arrive in Baltimore in The Gathering.
Untelevised Adventures: The Doctor says he once accidentally reduced the TARDIS' outer dimensions (such a thing occurred during Logopolis, though this was by no means a mistake). He likens the smell of the ocean to that of 'Riunian mines'.
Location: The inter-dimensional flux (i.e, out of conventional time), the planet Kapron, the USS Eldridge October 6th 1943.
The Bottom Line: "So we've landed in some conspiracy theorist's dream?"
A damp ending, undermined somewhat by Alan Barnes' more engaging and essential The Girl Who Never Was, and yet, even aside from the curiosity factor natural to all the Lost Stories, there's still something to be said for a story that looks credulously into the Philadelphia Experiment with such interest and attention to detail. Unfortunately, once through the dimension break, the citizens of Kapron are so clichéd you can almost hear the swish of their togas.