Rather than watching the two parts of the season opener a week apart, my husband and went to the theater showing by Fathom Events and saw both episodes for the first time back-to-back. It's hard to say how we reacted, because I came out loving it and he came out hating it. Now, to be clear, he did not get angry at the show - which is significant because he came out of almost every single episode of series 8, 9, and 10 on some - so that's good, but he thought it was awful.
So let's see, why did I like it? I'm trying to keep this short and I haven't thought on it very deeply, so I won't say much. The story itself was great, setting up a puzzling situation and then sending the Doctor and companions in separate directions to figure things out. The balance of power shifted constantly, allowing the TARDIS crew to perform well and succeed at what they were doing, only to have the next event set them back again. There was lots of action, as well as time shenanigans. I love it when the Doctor helps by going back after the adventure is over to plant clues - something that can't be done often narratively. I enjoyed meeting Ada Lovelace and the spy (I didn't really get what her name was - Nora? Noir?), but they seemed somewhat incidental to the plot; I wish they had both done more. The Master reveal was fantastic and I love Sacha Dhawan's Master - he has the ferocity and the cunning insanity that Missy was lacking, with just a hint of Ainley camp.
What did my husband hate about it? He thought it was boring from the start, with no action (other than the motorcycle chase scene, which we both agree was stupid - no one was afraid that someone was shooting at them, even with the bullets bouncing off their bikes, which for some reason took no damage). He felt that the entire thing was just talk. He had no interest in the historical scenes because he didn't know who Ada Lovelace was and so it had no significance for him, and he'd been spoiled about the Master (thank you, Doctor Who official Facebook page for posting "Congratulations to the new Master, Sacha Dhawan" on the day the first episode was aired; someone should teach you how to not spoil your own show), so that wasn't as exciting for him as it was for me.
We did both find Barton's speech at the end to be stunning, if hitting a little too close to home. One thing I loved about it, and this is a little hard to explain, but Barton delivered it in-story as a triumphant, gloating speech to the people he was going to kill by having gathered their data, but it also served as an indavertent (to him) warning to the audience -- as opposed a to lecture to both the in-story characters and the audience at the same time. Does that make sense? He wasn't trying to teach the world anything, but to us, it's a truthful message. Hm. Like I said, I can't really explain what I mean. I also loved how the audience, listening the speech, slowly changed from excited listeners to growing unease to horror, with some continuing to think it was all humor until the devices started attacking.
We also both groaned at the destruction of Gallifrey and the mention of the Timeless Child. Gallifrey - or the lack thereof - has been used too much as an emotional trigger ("Omg, they mentioned Gallifrey again!") without actually being a part of the show, and here we go again. Moffat brought it back at the end of "The Day of the Doctor" with the implication that the Doctor was happy it hadn't been destroyed and excited to go searching for it, only to not even mention it or that he even cared until the end of series 11. And the dropping of the Timeless Child thing felt exactly like Moffat's style of mentioning something off-hand every episode (the crack, the eyes, the Impossible Girl, the lady in the afterlife, the Hybrid, and to some extent the vault) and calling it a story arc. If the Doctor doesn't spend at least some time trying to either find out about the Timeless Child, bring Gallifrey back, or track down the Master, it'll just be the same old thing and I'll be very disappointed.
However, bottom line is that I enjoyed the episode and am looking forward to the new series. Yay, Doctor Who is back!