One of my all-time favourite moments in the Peter Davison era happens in this episode. After the TARDIS materializes, then quickly dematerializes, a puzzles Doctor wonders what went wrong. Turlough, who just seconds earlier was about to kill The Doctor, postulates, "Could it have been affected by a tangential deviation coming out of the warp ellipse?".
It's what The Doctor does during Turlough's question that amuses me. At first, he looks on with surprise at the futuristic technobabble that's exuding from this 1980s school boy. By the end, though, The Doctor just answers back as if everything was normal. He doesn't need to ask Turlough why he knows what a warp ellipse is. The fact that Turlough seems to know what he's talking about is proof enough that he is most likely an alien, or, at least, not the 1980s school boy he appears to be. It's a beautifully subtle moment that emphasizes one of those great characteristics of Doctor Who - ordinary objects or people that are far from ordinary.
There's another lovely moment when The Doctor attempts to jog the Brigadier's (the circa 1983 Brigadier, that is) by bringing up old friends like Liz Shaw, Jo Grant, and Harry Sullivan. This segues into a lengthy sequence of clips from past episodes (some of which the Brigadier was actually present for). Looking back at Mawdryn Undead knowing the whole of Doctor Who history, this sequence just looks like a clip happy sequence whose sole intention was to keep Ian Levine busy and placated. But, apart from the flashbacks The Doctor has in the moments leading up to his regeneration in Logopolis, the Brigadier sequence is the first full on retrospective sequence seen in the series, and thus the effect is rather charming.
The downside, though, is best exemplified by the fact that my first encounter with the Brigadier as a child was by watching Mawdryn Undead, so none of the clips made any impression on me in trying to job my memory. They were just a bunch of clips of strange beasts that I had never seen before. To uninitiated viewers, these clips could either alienate them or entice them to delve more into the series' history. Fortunately for my 12-year-old self, I chose the latter.