Continuity mistake: The time on the mantle clock behind the man carrying a shovel (as a weapon) changes several times, jumping forward or backward (e.g. 6:50 to 7:18 and 7:18 to 6:43). The clock behind Adam is sometimes coordinated with the other clock (@ 7:48), but other times is not (e.g. 7:52 vs. 7:18 or 6:43). (00:21:08 - 00:22:17)
Revealing mistake: The dog may be trained to go down the hallway, looking for a treat, but not to encounter Henry and "act" like he is happy to see a family member who just returned from vacation. Instead of being excited to see Henry, the dog's body language is indicative of stress or discomfort - tail pointed down with no wagging, slight cowering posture, weight shifted backward, and he even starts to back away from Henry. When lying next to Henry, the dog tries to crawl over the side of the bed. (01:17:45 - 01:31:00)
Other mistake: The scene where the king has directed his aides to issue "a firm denial of these accusations" makes little sense, since Alex has already officially and firmly confirmed their relationship from the White House press room. For the palace to announce that the son of the US president is lying would create diplomatic chaos between two very close allies and would not happen. (01:42:25)
Continuity mistake: Before going outside with Alex to meet the crowd, the knot in Henry's tie has one diagonal white (or light-coloured) stripe showing, which is near the centre. When Henry opens the door, there are two stripes showing on the knot - one near the top and the other near the bottom of his shirt's collar. (01:45:40 - 01:46:35)