Roots: The alternative Doctor's 'death' and regeneration are a deliberate mirroring of events from the Doctor Who TV Movie. Raiders of the Lost Ark (the Fuhrer's interest in Biblical totems such as the Ark of the Covenant and the Spear of Destiny). The Doctor quotes 1980s series producer John Nathan Turner ("the memory cheats").
Intertextuality: The Professor X story Vault of the Cyborgs is presumably itself a Who-universe equivalent of Tomb of the Cybermen, whose recovery and reception were viewed similarly in some fan corners (others of us were just grateful it was back at all).
Continuity: Near the end of World War Two in Klein's timeline the Reich through reverse-engineering Ace's walkman secured atomic technology and devastated New York and Moscow with (likely) hydrogen bombs, potentially ending the War. The Seventh Doctor returned alone (Ace having been executed) to Germany in 1955, but on exiting the TARDIS near a checkpoint in the West was shot (the guards mistook his umbrella for a rifle) and taken for dead. His body later went 'missing' (he having merely walked away following an un-witnessed regeneration - see 'Roots').
In 'her' 1962 Klein was a physicist researching at Cambridge University when she was contacted and recommended to Major Jonas Faber and delivered to Berlin for her expertise in classified projects. Under Chancellor H much material of extraterrestrial origin, including the remains of technology from as many as twelve different alien species, had been suppressed to avoid public alarm and appease the Fuehrer's own misgivings about alien races. Growing closer to Faber, Klein discovered the existence of the TARDIS and in attempting to gain entry to it activated a personal alarm pre-set by the Seventh Doctor to inform his successor. As the "handsome, in a gothic sort of way" Johann Schmidt he contacted Klein in a ploy to retrieve his confiscated TARDIS - Klein's role in this was not only to locate the TARDIS, but to effect travel back to 1944, the Eighth Doctor being unwilling to risk crossing his own time track. As Schmidt the Doctor was known to the party for his covert work spiriting resistance from captivity and undermining the Reich's ethnic cleansing programme. He claims to have picked up some temporal expertise in Copenhagen.
The TARDIS is in its TV Movie configuration, as confirmed by Klein, and set for Florana. The Doctor says it has no 'travel log' (possibly his reason for keeping a diary).
The Doctor recalls 1960s science fiction television programme Professor X (see: Links), claiming that the recovered story The Vault of the Cyborgs didn't live up to the reputation it garnered whilst missing. He has, via Klein, a rough approximation of his next incarnation's appearance (assuming these are 'fixed' despite alternative time lines, which this story suggests is the case).
Links: Colditz, The Three Doctors ("I've redecorated-" "-I don't like it"), Time Crash (leopard skin being the only 'alternative' interior environmental configuration (desk-top) available). Remembrance of the Daleks (Professor X), The Space Museum (time tracks), Doctor Who (see: Roots, the Eighth Doctor says to Klein "you'll do great things', echoing his alternative self's comment to Grace Holloway), the Doctor's "alien sands... alien life forms whirling in a different sky" speech to Klein recalls the First Doctor's similar speech to Ian and Barbara in An Unearthly Child. Klein's dismissive reference to "stranded space trolls" may have a small number of likely connections, perhaps the closest being the construct left behind in woodlands outside Copenhagen (see: Continuity) after Grand Theft Cosmos.
Location: [Klein's timeline] Germany 1944, [actual] The TARDIS, en route to Florana.
The Bottom Line: "Mankind has a breathtaking ability to sweep things it doesn't understand under the carpet of history."
The rounding out of Klein's character continues with an irresistible window into her quite plausible and equally fallible world, and her humiliation at being used by the Doctor to erase her own past timeline is palpable. This is a superior two-hander, and the surprise cameo of Paul McGann in a particular role is the sort of thing to make any fan grin from ear to ear.