What I liked:
That they took the Clara-becoming-the-Doctor theme that has grown over the last two seasons as far as it can possibly go. She is now just about as literally the Doctor as she could possibly be - immortal, unaging, with a stolen Tardis disguised as something ridiculous, running around the universe and going anywhere but Gallifrey, with her own companion by her side.
The endless references to previous stories and companions. 'Journey's End', 'The End of Time', McGann's DW movie, 'Impossible Astronaut', 'Listen', 'Utopia', 'Day of the Doctor', 'Time of the Doctor', the classic Tardis, probably dozens more I missed...
The deliberate fake-out with misleading spoilers. Making people think the Clara in the diner was a Timeline Splinter and the Doctor knew who she was, so that the twist that it was the real Clara and it was the Doctor who couldn't remember her would hit home. Well played.
The Doctor basically taking over the entire planet without saying a word or doing a thing.
The cross-race, cross-sex regeneration. Shouldn't she have had some kind of post-regen fugue though? They can't just change everything about their entire bodies and then go back to work like nothing happened.
What I Didn't Like:
So... is that it with Gallifrey then? All that build-up and we still have no explanation of where Gallifrey has been hiding (except for 'billions of years in the future') or how come the Doctor couldn't find it in 'Death in Heaven' or how the Master got out with some Time Lord technology. Nobody seemed to have any trouble getting in or out of it, so what is the big deal?
This story kind of tweaks the motivation of last week's episode - there we were told that the Doctor didn't know who was behind it and going through all that crap for 4 billion years was all so that he wouldn't have to tell the secret of the Hybrid. Now he says he knew it was the Time Lords all along and he went through all that crap because he knew he needed the Time Lords to be able to save Clara. Yeah yeah I know, Rule One. But it rather undermines the power of last week to then say it was something else altogether.
Was that the same incarnation of Rassilon as from 'End of Time'? Couldn't they get Timothy Dalton back? If that is the Timothy Dalton Rassilon just aged a hell of a lot, how come the General hasn't aged the same amount if 'End of Time' and 'Day of the Doctor' were basically happening at the same time from their POV? And if it's not the Dalton Rassilon, then the last time we saw him he was being attacked by Simm Master. So we are still left not knowing how Dalton turned into this guy, and how Simm turned into Gomez. And where does Capaldi's appearance in 'Day of the Doctor' come into it - is that still to come?
I guess all of this - the Doctor going through all the crap of last episode to get to Gallifrey, only to immediately steal a Tardis and run away again - proves once and for all that for all his guilt over killing them all, he really has no use for them aside from what they can do for him and his companions.
.