When Underwood walks us through building a fire, there are obviously at least two different takes: the logs first stacked are parallel but when they switch views, the log are now in a downward slant.
In the sequence back and forth between Aidan at the computer and Claire and Tom in the White House the events are supposed to be taking place at about 4pm. The shots of Aidan's computer show time moving along as one would expect. However, in the first cut-away to Claire and Tom, his watch shows 11:07. Back to Aidan and it's 4 something. Back to Claire and Tom, presumably moments along in their scene, and the watch shows 11:25. Back to Aidan and it is getting closer to 4:30.
The text message shown at 0:38:14 includes the word "cemetary". The correct spelling is "cemetery".