(at around 47 mins) During a conversation with Ben at his school, Christine drops her bag to the floor and approaches Ben to give him a hug. Camera cuts to wide angle of the whole classroom with the hugging couple yet there is no bag on the floor.
(at around 33 mins) When Christine discovers about her son, Adam, for the first time and she documents that on camera, saying, "His grief isn't new, but it's new for me." However, when she wakes up on the next day and checks the camera videos, what she said is changed to, "His grief isn't new. Mine is."
Just after Christine wakes from a nightmare, we hear Dr.Nasch on the phone explaining he's a neuropsychologist at University College, London; but in the next scene she sees his name badge, which shows he works at Westland Psychiatric Hospital.
Christine first records a video of herself saying, "You're my lover, you're my protector, and my life is nothing, nothing without you." A moment later, she plays the same recording back to her husband, but this time it says, "You're my lover, you're my protector, you're my... you're my everything." Later on, she plays it back again, and again it is slightly different: "You're my lover, you're my protector, you're my everything."
During the scene at the cafe in the park, when Christine and Claire are discussing Ben, the background keeps changing from near to long range. 'The Gerkin' appears in long range between the two characters one minute, then it has completely disappeared the next. There is a also a lady sitting behind to the left of Claire, who has vanished when they stand up.
During the first time Dr.Nasch is driving, in a right-hand-drive car, the car is shown coming around a long right curve in a parking garage and he is on the right (wrong side of the road for England). However, that isn't a two-way road - it's simply the Down ramp into an underground garage, where the exit is a separate Up ramp.
Claire tells Christine (while the latter is at home) that she can meet her at Greenwich Observatory and be there "in an hour".
As Christine was taken to Ascot District Hospital from home, it is reasonable to assume she lives in Berkshire - and therefore would not have been able to reach Greenwich Observatory in less than an hour as she is seen waiting for Claire.