Melvyn Douglas's apartment is plainly a set, not part of the building that Joan Crawford enters. The fireplace is on the same wall as the entrance door, so a corridor is on the other side of the wall. There would be no room for a chimney.
Melvyn Douglas says that even the queen of England takes time off, even though at the time of filming it was King George VI on the throne. He probably emphasised the gender for effect though.
At c.4 minutes, the truck driver forgets to put up and secure the rear door ramp when he drives off.