For the opening shot, it definitely seems like they took inspiration from the Star Destroyer shot from the original Star Wars.
I find it kind of funny that the Doctor's arrival triggers an amber alert.
The Doctor claims the presidency of the High Council of Time Lords, so between that and him supposedly working for a mysterious trio, clearly something is very wrong with the universe.
Also, K9 called the TARDIS "a very stupid machine" - not sure if that's jealousy on his part. (I'm guessing the TARDIS is explaining what's really going on in a way that only K9 can understand)
Tom Baker does a good job at making the Doctor seem scary and erratic.
I'm guessing that the material that the Doctor demands to be put "everywhere" is going to be crucial to stopping the alien plot. (though maybe it's just a sign of how he's acting mad with power)
Leela's response to being asked to not kill anyone during the Doctor's induction ceremony ("I will try") is great.
"Honoured members of the High Council, Cardinals, Time Lords, madam..." Really showing off the bigotry of the Time Lords with that one. (seeing as they single Leela out seemingly just because she's not one of them)
By the time that they got to the Great Key of Rassilon, I figured there'd be a dozen or so ___ of Rassilon that the President had the right to.
I wasn't expecting a Time Lord inquisition.
I like how we see the Doctor ignoring Leela's attempts to be let in even though it pains him to do so, rather than having him keep up the insane or volatile act throughout when he's on-screen.
Thankfully for K9, Gallifrey is wheelchair-accessible.
I can't tell if the Doctor is laughing maniacally at his "plan" succeeding or Tom Baker is laughing at the special effects used for the aliens. (which looks like sheets of tinfoil on a green screen)
So far, this story reminds me of Silver Age comics where the artist came up with an outlandish/absurd cover and the writer had to figure out how to work that into the plot.

Strangely enough, a lot of them involve Jimmy Olsen and gorillas, as was the style at the time.
"You talk always of surrender. Are all your tribe like this?" I'm honestly surprised that Leela stays on Gallifrey, as she's clearly not a fan. (apparently she falls in love with Andred, but so far, they've had one conversation which boils down to "don't kill anyone" "I'll try")
The Doctor clearly knows that the Castellan is scheming against him, but I'm fully expecting that he'll put one of the troublemakers that the Castellan lists in charge during his absence. (he still is referred to as the Lord President in the 5th and 6th Doctor's time, or at least he calls himself that as 6, so I'm guessing the title sticks)
Finished part 3 - Leela seems to get along with the Gallifreyans/ex-Time Lords living out in the wastelands, at least.
It's a bit later than I thought, but I'm starting part 4 now.
"But you have access to the greatest source of information in the universe!"
"I do talk to myself sometimes, yes." XD
This story does a lot of that gag where a character says something, and then we cut to something that immediately contradicts it. ("We have suspected the Doctor since we first met him." cut to the Doctor "Well, at least they don't suspect me.")
It's funny that, as soon as the Doctor says that K9 is in charge, K9 seems to ALSO go mad with power haha.
I'm guessing Leela's TARDIS key was taken away and I missed it.
The Sontarans were the masterminds behind this? (and they invaded Gallifrey before the Daleks did - good for them)
The Sontarans in this story seem to hiss out their s's.
It says a lot about Leela's skill that she can effortlessly kill a Sontaran moments after learning about their weakness.
I'm on episode 6. I'm surprised that a Sontaran took his helmet off; going by the glimpses that had already been seen, I thought this episode might not have had the budget to do that. (you could see the actor's skin beneath the glimpse of the Sontaran skin)
The actors seem to talk into the camera a lot in this serial.
I get that it's to save money by reusing the same set (and it makes for a fun little gag), but the Doctor (or the TARDIS) really should put signs up for the storerooms.
The Borusa actor in this episode seems to be enjoying himself the most out of the Borusas that I've seen. (I know it's a bit of an accidental running gag that he's played by someone different in every appearance - I've seen him in The Deadly Assassin, the Five Doctors, Arc of Infinity, and this, though I don't really remember him from Arc of Infinity)
A Sontaran lithely leaps over the corner of the pool only to trip over a chair.
I'm not sure if it shows how desperate the situation is that the Doctor is walking through the hallways of the TARDIS with a gun or if it's just an out-of-character plot point. (probably a bit of both)
Though I feel like the Doctor got more anti-gun after the Time War; 6 did shoot a Cyberman at one point. (he didn't necessarily approve of them during his time with UNIT, but it's not like the UNIT soldiers had any other method of defending themselves)
Stor is willing to sacrifice the entire galaxy (not sure if they're using the wrong term here - maybe they meant solar system? The series seems to use "galaxy" interchangeably with a lot of other space terms), his battle fleet, and his own life just to make it so the power of time travel can't be controlled by anyone if the Sontarans can't control it.
Makes sense why they were kept out of the Time War. (though how that happened, I have no idea - then again, the Doctor somehow trapped an alien in every mirror)
"Staying? Here? Why?" My thoughts exactly.
I was hoping Leela would serve as something of an ambassador between the Time Lords and the people in the wilderness; her being in love with Andred seems hard to justify when they had two conversations with each other at best.
Romana and K9 mk. 2's exit was about as abrupt as Leela and K9's, though at least Romana more or less became the Doctor for another universe. Leela volunteered to stay on an elitist xenophobic society that would treat her far worse than the Doctor did. (and the Doctor didn't treat her all that well compared to his treatment of someone like Jamie)
Kind of rude for the Doctor to respond to Leela's comment of "I will miss you" with slamming the door in front of her. (though he does say "I'll miss you too, savage" once the door is closed)
Finished! Out of the classic companion exits that I've seen (Susan, Jamie, Zoe, Jo, Sarah Jane, Leela, Romana, and Nyssa), Leela's felt like the worst to me. Susan and Jo left for similar reasons, but at least in those cases, there was some build-up. Jamie and Zoe's exits were tragic, and while Sarah Jane's was rather abrupt, I thought it worked well with
the way that Jamie and Zoe left being taken into account.
I recall not being thrilled with Nyssa's; I went back to my comments on that episode, and I felt like it was very abrupt. Still, I feel like Leela's was worse because it felt out-of-character and left her in a situation that seems like it would quickly become bad/frustrating for her.