This is all set up by having a montage of her trying to juggle them, running from one appointment to another like some nineties teenage sitcom. That said I liked the vague hints at various adventures the Doctor and Clara go on that we don't get to see, and what that means for the extended universe. At some point I'll probably do a post about how Moffat has done this, and just why it's so handy for the future of the series.
However, it was not what I expected from the first meeting between the two. I expected it to be all about the Doctor's inability to see past Danny being a soldier, and how that shouldn't be the type of man Clara should be with. We did get that, including the rather brilliant aspect of the Doctor's complete inability to process the fact Danny's a Maths teacher, because as an ex-soldier he should be Physical Education, and his assumption that Clara's boyfriend was the bookish English teacher who shares a few similarities, even dress sense, to a certain previous incarnation.
But it was so much more than just the Doctor not accepting him. The unexpected part is the the Doctor is having to prove himself to Danny as well. The scene when Danny realises just how the Doctor thinks, and starts responding like a soldier to a high ranking officer, pushing and pushing the Doctor into losing his temper with him was probably one of the most important in the episode. Because Danny has seen danger, and war, and how you should deal with that, and he's not seeing that with Clara, and that she should be scared.
It seems, at least initially anyway, that we're getting back into the territory we had with Rose and Jackie, that of a loved one trying to warn you that travelling the Doctor is not as good for you as you think. Where Jackie saw her baby girl going into constant danger, Danny sees a superior officer willing to put his companions life on the line in order to stop evil, and he doesn't like it.
More importantly, by the episode's end, neither has accepted the other. They've just met and for the Doctor, he's started to because the Soldier proved he would put himself in danger to save both Clara and the planet. As Danny said “It doesn't matter if he likes me, or hates me, what matters is whether I'm good enough for you.” But the Doctor hasn't done anything to prove himself yet.
As for the rest, of the episode. It was forgettable. Though a copper in a junk yard in an episode all about Coal Hill school has some imagery connected to it. Thhe fact they just outright admit it with the Doctor saying “Home Sweet Home” a few minutes later slightly ruined the nod for me. Especially after the masterful version in 'Day of the Doctor'. On the flip side I was sort of disappointed there was no talk of the Dalek attack on the school, or a visit from one of the Governors.
I wasn't so keen on the invisibility watch either, mainly because for the Doctor to have something like that just laying about the TARDIS seems a bit too trite. It's too powerful a device just to pull out now, there's plenty of times he should have that. Where the ability to run around invisible would save the day. It's not psychic paper which just bypass' some unneeded story beats with a smile, but a big piece of tech. The episode used it well, but it's too big a macguffin to just forget. Of course, this is where Moffat pulls it out to be super important during the finale in five weeks time.
'The Caretaker' is by no means as brilliant as 'Listen' or as balls-out fun as 'Time Heist'. It will never be remembered as a classic, but it is an episode that needed to happen for the characters, and it did its job well.