Chancellor Flavia is, by the end, the only surviving member of the High Council of Gallifrey, allowing her to declare the Doctor the new Lord President by "a unanimous vote of the full High Council". The Doctor then tells Flavia to return to Gallifrey and grants her full presidential powers until his return. This means that the entire power of both the full High Council and the Presidency of Gallifrey were in the hands of one single individual!
Why doesn't the First Doctor recognise the Master even though it's already established that Time Lords recognise each other across regenerations? Because the Ainley Master is a stolen Trakenite body, NOT a real regeneration! (Why is the Master surprised? His ego can't accept that the Doctor isn't as obsessed with him as he is with the Doctor.)
Fridge Horror: OK, Borusa deserved it, but what about the other "immortals" on Rassilon's tomb? What if they were timescooped victims who had survived the death zone and reached the crypt? They wouldn't even have received the cryptic warning because they couldn't read Old High Gallifreyan. Wouldn't they have just thought they were being offered a prize they'd legitimately earned?
They're all wearing Time Lord regalia, though, suggesting that they were also Time Lords with stories similar to Borusa's.
The Game seems to work like this: the Time Lords scoop up various unsuspecting warriors from various points in time and space. The Time Lords then direct these warriors to act as their "pieces" from the safety of the Capitol. Whichever Time Lord's "piece" reaches the tomb first is the winner, so that Time Lord is then teleported to the tomb to receive his or her "prize". The warrior is then presumably dumped back where they came from or, more likely, just disposed of. In any case, it's almost certain that none of those Time Lords were ever in the Death Zone personally.
Sarah Jane doesn't seem to recognize the Fifth Doctor as the current Doctor during the events of this story. It doesn't help that she never gets to so much as talk to him as she's promptly carted off with the Third back to home. In School Reunion, when she realizes who the Tenth is, she shockingly exclaims "I thought you had died!". While they were swapping stories about whose Doctor is more of a pain in the ass, Tegan should have filled her in on who the young guy in the cricket outfit was, so why did she think that he was dead. It was true that the Doctor that she spent so much time with had died and regenerated since but that wouldn't have been what she meant as having died, since she had seen the Third regenerate into the Fourth. She thought "The Doctor" had died. Also, Sarah Jane has obviously been keeping track of what UNIT has been doing, even long before School Reunion and the followup Sarah Jane Adventures, so she would have known that although the Doctor had definitely moved on and probably forgotten her for all he cared, he was still out there somewhere and she was just meant to go on with her life. Also, why doesn't Sarah go home by going aboard the Fifth Doctor's Tardis since unlike the Third Doctor, she was scooped up from the present. The Third Doctor was headed back to whenever he was scooped up from which can't be the present since the Brigadier is obviously older too so there goes the idea of the UNIT stories taking place in the 80s.
Presumably, she thinks that he died some time later. Besides, as far as she knows, Tom Baker was the latest Doctor. It's not as if the Doctor ever talks about what order his bodies were in.
As to why she doesn't go back with the Fifth, why would she? As far as we know, the Third dropped her off whenever she was meant to be. Since he recognizes her, his TARDIS is (as much as it ever is) fully functional at that point.
The Second Doctor doubts Jamie and Zoe are real because "the Time Lords erased your memories of the time you spent with me, so how do you know who we are?" But the Time Lords didn't erase the Doctor from their memories completely, they let each of them remember their first adventure with the Doctor, only erasing starting just before they started traveling with the Doctor. Yes, Jamie shouldn't have known who the Brigadier was, but the real first clue should have been the fact that Jamie knew who Zoe was — her first adventure included Jamie, so she'd know him, but Jamie didn't meet Zoe until well into his travels, so he should have no memories of her!
Because if he'd said all of that, it would've sounded really clunky.
