When Jacob is sending a text message to Sam in Anna's kitchen, upon being questioned who he is "texting", he sets his phone down in front of the laptop computer on the table and leaves the room. In the next shot, Anna goes to browse his text messages, and the phone has changed its position to the side of the computer instead.
When Jacob receives a text message from Anna while lying next to sleeping Samantha and Anna lying next to sleeping Simon after sex saying, "Hi". Even though when the camera shoots over to Jacob it shows that Anna actually text-ed Jacob saying "Hey J", and Jacob was the one who text-ed saying "Hi".
In the first part of the movie Anna and Jacob are using an old flip phone. When Anna is back in London in a taxi listening to Jacob's voicemail she uses an iPhone but later when she is in bed calling Jacob she is back on her flip phone. In all scenes after that Anna and Jacob both use an iPhone.
When Anna sticks her presentation paper under the windshield wiper of Jacob's car for the second time and walks away, it is stuck with a tiny corner towards the middle of the wiper. In the next close-up shot the paper is stuck with a much bigger corner under its tip.
(Around 42:40) When Jacob and Anna are on the Piccadilly line service to Heathrow, first Jacob's suitcase is at his left, then at his right, and you can't see it on the reflection at the glass behind Anna.
When Jacob is at a club with his current girlfriend, Samantha, he receives 3 texts from Anna that were first sent on December 1, 2010 but her last text was sent on May 29, 2011. This sequence of texts were supposed to be sent all within 5 minutes of each other according to the plot, not 6 months.