What was up with the 4 knocks when the Doctor was in her cell? Are we led to believe it was Jack trying to communicate with her before seeing her in person? I wouldn't be thinking much into it if it wasn't 4 knocks, which has a direct relation to the Master. But nothing was really done with it, nor do I think anything will (or even can?) be done with it in the next series.
If I have my info correct, the Doc was in prison for 79 years. Looks like Big Finish will have some more ample room to play with once they can do 13 Doc stuff.
Okay so I know it's only a cameo and not the point of the episode, but having a Silent in prison is a fun concept that should have been played with more. Like, do the Judoon have technology to remember Silents? Do the prison guards (whoever they may be) get surprised everyday to see Silents in a cell? Come to think of it, this episode could have really been more fun if the Doctor escaped prison by using the various aspects of each alien to escape, rather than Jack showing up with a deus ex machina way to get out. Oh well.
I liked how Jack Robertson had no arc and remained the same throughout the episode. Which is generally odd since stories work great when a character changes, but it can also be interesting to see a character double-down on who they are when given the chance to change. And Robertson had a few opportunities to redeem himself, and he kept choosing to be the slimy businessman/politician. At least Chibnall didn't make many (or any?) strong, obvious parallels to Trump, but it's hard not to associate Robertson with him when… you've been around for the last 4 years.
Loved the bookending of Ryan and Graham's arc for this show, with them trying to get Ryan to ride his bike. And that Ryan wore a yellow beanie after the Doctor's comment. "If anyone could pull off a yellow beanie, it'd be Ryan".