During the reindeer games, when Colin walks in, Claire's antlers have rings on them and then as the scene progresses the antlers become bare followed by the antlers having rings again.
As the van arrives to drop the children off for school, the van is on the left side of the road as the would be in Britain, however the markings on the road, specifically directional arrows, are clearly intended for traffic that would flow on the right side opposite of British traffic norms.
In several scenes set outdoors, the call of the eastern wood-pewee which would 1) not be where there is snow/winter weather 2) in Europe as its range is limited to North and South America.
When Princess Rose is making the kids sandwiches, a fly is crawling on the ham. Eventually, the ham disappears, presumably removed from the set to discourage the fly.
On Christmas Eve, when Claire and Mrs. Lansbury on the bench Mrs. Lansbury shows Claire a video. The video screen size changes, you can see a green screen background for a second and at one point the screen is bigger than the phone.