Corrected entry: Bill grabs an umbrella as a makeshift weapon before entering the bathroom of her flat. After she enters and finds the bathtub wet, the umbrella has vanished. (00:24:20)
Corrected entry: When Bill bursts into the toilets at the Sydney restaurant, the door is shown swinging inwards, and during her and the Doctor's subsequent conversation, the hinges are shown to make the door swing in. When Heather arrives and the two flee the toilets, as the Doctor yells for the restaurant patrons to get out, the door suddenly swings outward. (00:35:55)
Correction: Some doors swing both ways. It is common in restaurants.
Not only is this the door to a toilet, the hinges are visible on screen, and they are normal, one-way hinges, not the kind you'd find on restaurant doors.
The mistake is indeed wrong. The door hinge we see may appear like a normal hinge with knuckles and pin, but it's actually a double acting spring hinge that allows the door to swing in both directions. Also, there is no door knob hardware, only a swinging door push plate on the door. I've personally seen women's restrooms which have an outer swinging door with fully enclosed floor-to-ceiling inner cubicles (we see their "reflection" in the mirror) such as the ones shown.
Sorry, forgot to include the link: http://www.projectgalleryla.com/wp-content/uploads/2018/01/Cafe-Door-Pivot-Hinges-Home-Depot.jpg.
Looking at the scene again, that would explain why the side of the hinge is visible in the shot where Heather bursts out of the bathroom. It's still a) not very clear on camera, and b) really weird to have that kind of door on a bathroom.
That's right, it's exactly the reason why we're able to see the barrel of this type of hinge when Heather opens the door outward. And I agree, I also think it's really weird to have that kind of a door on a bathroom. Go figure why some establishments have done that.
Correction: We see the umbrella leaning against the towel rack at the wall beside the bathtub. Bill placed it there while offscreen at the start of the closeup of the tub drain, before her hand appears.
Super Grover ★
Rewatched the scene and spotted the reclusive brolly - you are, indeed, correct.
skater49th