(at around 1 min) In Bridget Jones's Diary (2001), we learn that Bridget's birthday is November 9th. This third movie opens with Bridget's birthday suddenly moved to May 9th.
(at around 1h 16 mins) In Bridget Jones's Diary (2001), we learn that Mark is four years older than she is. When Mark is checking their compatibility on Qwantify, it says that he is 50 years old and Bridget 43. He should be 47.
(at around 1h 40 mins) When Jack takes over carrying Bridget to the hospital, he leaves his motorcycle helmet on his bike. He then carries her together with Mark and does not have his helmet when they enter the hospital. Later, when he is waiting in the hospital, his helmet has magically joined him there.
The first Bridget Jones film (Bridget Jones's Diary (2001)) has the main character as 32 years old and this was filmed in 2001. The third Bridget Jones film (Bridget Jones' Baby) she was 43 years old and it was filmed in 2016. If the film took place 15 years later, she would have to be 47 years old and not 43.
(at around 2 mins) At the very beginning, as Bridget is lip-syncing to the rap-music, her glass of wine shifts several times between almost empty and quite full. This is extra clear when the glass is almost empty and then she spills wine just after getting to her feet.
When Bridget receives her third trimester scan, the Dr places the ultrasound wand and the full size of the baby can be seen visible on the screen. At this point in the pregnancy, the scan would only show various body parts and scanning of the whole abdomen would be required to see all of the baby.
(at around 1h 16 mins) When Mark is checking his compatibility with Bridget (vs. Jack Qwant's) on The Qwantify dating website he types in Jack's name as "Quant" not "Qwant".
The footage used to show Bridget returning home was taken from the first movie as the taxi shown in the shot is a Vauxhall Cavalier which was last produced in 1995 and so the car would have been over twenty years old at the time the film was made.
(at around 1h 35 mins) After Bridget leaves the ATM and finds Mark on the street, what she tells him is not in sync with her lips.
(at around 1h 26 mins) Bridget lives by London Bridge station and Mark says he lives in Ealing. In one scene, Bridget leaves her flat and walks to Mark's house. This would be a walk of more than 10 miles.