Beware of unmarked spoilers — Headscratchers pages are always Spoilers Off
So why didn't the Doctor run to catch up to the hooded figure to find out who they are? Or at least call out to them? I know he wants to get back to make sure Ruby is OK but he's a time traveller so it's not like time was of the essence.
It's none of his business, especially because it would be hiding something so important to Ruby that he purposefully found out which is very different to already knowing who it is, and this means that he's letting her have control of the situation.
On top of that, the Doctor knows that sometimes having that information doesn't make things better. Learning they were the Timeless Child was traumatic for them, and they may never truly know where they came from; knowing who the hooded figure is and why they abandoned Ruby could very well just make her deeply unhappy without giving her closure. We also actively see how much worse her mother's life is without Ruby having been there — both Ruby and her mom are very happy. To top it all off, if Ruby wants to find out who her birth parents are, that's another story, but having people know things about who you are and actively hiding them from you? The Doctor's not a huge fan of that.
There's also the fact that the Doctor interacting with Ruby's birth mother shortly after Ruby was dropped off at the church could affect the timeline again in some way...a risk that the Doctor doesn't want to take, especially since he has just fixed the timeline.
Who the Hell is Mrs. Flood, given that she didn't recognize the blue box at the start of the episode, but figures out what it is after seeing it in use?
She could be playing games, and given the aquatic nature of her last name, might be someone very familiar with the Doctor in a new guise.
She could also be the one who picked up the Toymaker's gold tooth, which housed the Master...perhaps she could be a Time Lord, specifically the Rani?
She could also potentially be Ruby herself from the future…
Or someone who met the Fifteenth Doctor in her past but his future.
Or she could be the Master.
Or perhaps she could be a very old Susan?
How does the Doctor know about tree falling on Davina McCall? If I recall correctly, it was never mentioned during the entire episode. You might say "Ruby told him" but that bring another question. How does Ruby know? For what Ruby knows Davina might just as well just lost signal. I would call it an Ass Pull but maybe I missed something.
Davina calls her up to tell her she's been having a run of freakish bad luck before she screams and the line cuts off, and then the Doctor confirms that all the bad luck was caused by the Goblins, including Davina's. Even if you don't get "crushed by a Christmas tree" from that, you'll probably get "something bad happened to her." It's also possibly the case that Davina was killed by the Christmas tree originally, before the Doctor went back and changed it — in which case, all he'd need to do is check the news.
How was Doctor capable of pulling the goblin ship down? He mentioned that the gloves are carrying his weight but somehow I am not willing to believe that one averagely sized man is capable of outweighing the entire ship capable of carrying Goblin King and arguably few hundreds of smaller goblins.
The Doctor states that the gloves can be reversed so that, instead of making the wearer lighter, they make them heavier. So they increase his local relative mavity, allowing him to essentially become much, much heavier than the ship and pull it down.
How does one measly human baby feed an entire horde of goblins and their Adipose Rex king?
My understanding was that the baby was meant for the King alone.
Veering into WMG territory, but we see that killing the King makes all of the goblins disappear, so they're clearly linked to him somehow, maybe when he eats it sustains all of them as well.
