In Bridget Jones's Diary, we learn that Bridget's birthday in November. The third movie opens with Bridget's birthday suddenly moved to May. Bridget's birthday is November 9th in Bridget Jones's Diary, but it is May 9th in Bridget Jones's Baby.
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 Diary) 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 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.
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.
The goof items below may give away important plot points.
When Bridget is in the hospital holding her newly born baby, the baby is swaddled in a blanket and nothing else. The camera cuts to other characters for a second then cuts back to the baby, still in Bridget's arms but now in a newborn sleeper and wearing a hat.
Whilst Bridget appears to be living in Borough, close to The Shard and south of the River Thames, when she goes into labour her journey ends up at UCH (University College Hospital) in Euston, 4miles north of the river going via Albert Bridge which is in the opposite direction, well, quite a detour more than doubling the distance.
A newspaper seen on a bench a year after Bridget gives birth states that Daniel is found alive one year after a plane crash. Daniel's memorial service happened shortly before Bridget got pregnant, so the time span between the plane crash and the rescue should have been at least 21 months (and probably a few months more, allowing for time to search for and presume Daniel dead before the service).
When Mark and Jack argue after leaving the prenatal clinic, Mark uses the phrase "prenatal wind" which relates to why Bridget went to the clinic, but Mark was not in the room when Dr. Rawlings gave Bridget that diagnosis and nobody mentioned it after he arrived, so how did he know?