While talking with Cora prior to sleeping, the candle on Robert's bedside table disappears and reappears with only the flame visible until finally he blows it out, at which time it has reappeared completely at the edge of the table.
In the first airing Robert refers to the dog as "boy". In the rest of the series that have Isis, the dog is always referred to as female.
When Daisy wakes the staff up she says it's six am but it is full light out even though it's set in April. At six it would probably be starting to get light, but not as light as it actually is.
Lord Grantham refers to his dog as "Boy" in a library scene, though in later seasons his dog Isis is a girl. However, the earl owned multiple yellow Labrador retrievers, and the dog shown in the first season was a male dog, Pharoah (although he is never referred to by name). In the two years between the events of the first and second seasons, Pharoah presumably died, and the earl now has a smaller younger, female lab named Isis. The replacement was done out of necessity as the dog who lived in Highclere Castle, where Downton Abbey is filmed, was agitated by the presence of strange male dog around the house.
In Cora's first scene, she is in bed reading The Sketch. In the later seasons she tells the editor of The Sketch that she never read it until her daughter became a contributor.