While the story is set around November 1918, the outdoor shots were clearly taken in summer: The trees are full of leaves, the lawns are in their brightest summer green, and the characters walk in the open without coats.
While Matthew is sitting in his wheelchair, talking to Mary in the front garden, he moves his knees several times despite being paralyzed from the waist down.
The clock which is the focus of Armistice Day and ostensibly is chiming at 11am is actually a timepiece which does not strike or ring at all, as evidenced by the single winding hole.
When the family, staff and officers gather to commemorate the armistice, their attention is centered on the clock about to strike 11. Just before the chimes begin, this clock is shown in a close-up shot to be a tabletop clock. However, several long shots of the room, including during the sounding of the 11 chimes, show a freestanding grandfather clock against the wall behind the earl's right shoulder, which is also showing 11 o'clock and would be ostensibly chiming as well.
When Robert announces the armistice he says it will take effect on the morning of the 11th. At least a day passes before the household gathers to mark the end of hostilities. The armistice was not signed and announced until around 5:00 on the morning of the 11th so it would have taken effect only hours after it was announced. Also, the armistice was scheduled for 11:00 am Paris time. It would have been 10:00 in England.
When talking to Patrick Gordon Edith says that Robert found an aunt in 1860 who married a Gordon to and that might be how the two connect. She makes it seem like 1860 was a long time before, but would have been less than 60 years before and the woman would have had to have been either the sister of Roberts father or grandfather not someone who lived a long time before.
All through the war Lord Grantham asserts his authority that Downton is his house and he makes all the decisions about it. The doctor even asks permission before he makes decisions about what happens at Downton when it's a hospital.
Yet as the war is ending, Mrs Crawley announces that Downton will continue to be a recovery hospital long into the future, and they're all terrified they won't be able to talk her out of it. When did Mrs Crawley get the right to make any decisions about Downton whatsoever, let alone monumental ones like this. Her son is the heir, but even he has no say in how Downton is run, let alone his mother.