The, er, side effects of immortality have been pretty thoroughly (and well) explored by Highlander, so this episode just left me feeling like it was simultaneously too much and not enough. That is, they tried to cram too much in, but at the same time made it all too simple.
Maisie Williams is back as the girl the Doctor saved by making her immortal last week. She's lived a long time and has forgotten a lot of it, apparently, though she somehow remembers the Doctor pretty clearly, and Clara. Are we supposed to think this is what she held on to when everything else spun away? Lives, centuries . . . I feel like they didn't quite make that point, but it's what I infer.
And the years have made her hard, unsympathetic to her fellow humans, and generally unlikable.
The Doctor turns up looking for an amulet that Maisie (her name in this episode seems to be in question; the Doctor calls her by her Viking name, which she disdains, only referring to herself as "Me," so I'll stick with Maisie) is also searching for. She's teamed up with what appears to be Ron Perlman's Beast, who comes from a planet of anthropomorphic lions, I guess? He's promised to take her away to new worlds, but he needs the amulet to open a portal or something.
The episode boils down to: Immortality is cool so long as you have wheels.
And by "wheels" I mean transportation in general. The flip side being, immortality is not fun if you're stuck in one place. (Living chronologically may also lose its luster after the first few centuries.)
The amulet is found. Maisie asks the Doctor, repeatedly, to take her with him. She's his first choice; Lion King dude, originally her only option, becomes Plan B. But of course the Doctor refuses her, so Maisie and the Beast must go to a hanging and capture, I dunno, the death of the condemned or something.
Of course the Lion King has no intention of taking Maisie anywhere, and the portal that opens actually is intended to, what? Open the way for an invasive army? Rather like The Avengers?
Maisie has an abrupt change of heart in this moment, and not (one is meant to believe) simply because she's been lied to by Sir Roars-a-Lot. "I do care!" she shouts, meaning she actually does care about the people in the world . . . ? It's actually not at all believable in terms of character development. It's too sudden and not earned.
She and the Doctor are able to reverse the amulet and close the portal by using the second Immortality thingy on the dying man. I guess now he's immortal too? (Truthfully, he was the best part of the episode, a highwayman named Sam Swift, played to the hilt by Rufus Hound—just fabulous.)
Later, the Doctor explains to Maisie that she can't be his companion because two immortals together lose touch; they need to see through the eyes of mortals to tether them to humanity, etc. Though one has to wonder that the Doctor always chooses a human companion, and one from our current era besides. He could surely choose, well, anyone from any place or time, right? Why must he be "humanized" rather than "Some-other-planet-ized"?
The Doctor tells Maisie he'll be watching out for her. She tells him she'll be watching out for his companions, the people he leaves behind, broken in his wake. And then we get a lame moment of Clara showing the Doctor a selfie (that wasn't really a selfie because someone else clearly took the photo) just so we can see Maisie in the background. Ugh. So cliché.
I guess the point is to leave the door open for more Maisie Williams if/when they have use for her. But her character really would fit better in Highlander than Doctor Who.