When JJ and Jess go to her special spot near where her sister went missing, they watch some swifts flying above them. Swifts are migratory and winter in the tropics and would not be flying in the UK between January and February when the film is set.
The suicide pact made between the characters is established for period New Year's Eve - St Valentine's Day. When Martin and Jess meet her father opposite the Houses of Parliament, the clock on the tower of Big Ben shows 4.40pm. At that time of year it would already be dark but it is bright and sunny.