When Philippa takes the train to a lecture, travels on an LNER Azuma train. These weren't brought into service until 2019 and the LNER brand came back in 2018, replacing East Coast & Virgin Trains East Coast respectively.
The moquette for the train seat is also ScotRail and not LNER.
When Phillipa's manager Tony is giving her the HR talk, he closes the laptop and sits down at his desk. When he is next seen, a moment later sitting at the desk, the laptop is open about a quarter of the way.
Professor Sir Robert Burgess would not have been addressed by staff as "Mr. Burgess". He received his knighthood in 2010. In fact, most people who worked at the University simply called him "Bob".
The University of Leicester would not have been referred to as "Leicester University" despite characters and printed material (marketing banners, hard hats, etc.) referring to it as such.
When the car pulls away after picking up the kids from the house, the road reveals a dry patch, but the car had no signs of being wet.
Philippa Langley's ex-husband and two sons go to a local cinema to see the James Bond 007 movie SKYFALL, before King Richard III's body was exhumed in September 2012. However the London première of SKYFALL was on the 23rd of October 2012.