When Katharine enters the office at the office at 04:10 she places a pastry onto some sort of equipment. She then gives some to her colleague and puts it back on the equipment. From there it just vanishes and appears at 05:10.
Set in 2003, but no one is depicted smoking cigarettes in the police station, newsroom, homes, or government offices. Some workplaces had begun voluntary bans on indoor smoking at this time so this is not entirely implausible, but it is still somewhat anachronistic.
At around 1hr 16mins, James from the human rights organisation, Liberty calls Katherine. In their conversation he uses the expression 'going forward' meaning in the future. This expression really wasn't in use in the UK in 2003.
In a top secret facility, there are never removable disc drives, as shown in the movie. It's too easy to intentionally, or unintentionally, remove files to the outside.
When Katharine enters the police station, the first thing the duty officer says to her is "Handbag" followed by other personal items. Normally the first thing the officer does is to confirm the suspect's name followed by declaring the crime they've been arrested for.