The slime on the doors of the TARDIS appears and disappears between camera angles in the opening sequence.
When Clara says she is thirsty, Strax places the bucket of water on the desk in front of Clara, it is there in the following shot, but it disappears into the next shot without Strax or Clara moving it.
The Doctor finds a newspaper saying there have been 4 cases of spontaneous combustion reported. In the very next scene, Vastra states there have been 9 reported cases. While it's possible The Doctor found an old newspaper, or that Vastra gained knowledge of cases that had not yet been made public, she then turns around her display board to show Jenny a map with pins placed in it to mark the locations of the incidents and there are more than 20 pins.
The opening shot shows a Tyrannosaurus standing as high as the Westminster Clock Tower and Madame Vastra says "dinosaurs were mostly this size". The Clock Tower is 316 feet high, but the largest Tyrannosaurus specimen ever discovered would have stood only 40 feet tall.
Clara doesn't appear to know who the regenerated Doctor is, and thinks he is somebody else entirely. However in The Day of the Doctor (2013) she met two previous incarnations of The Doctor and seemed to accept the fact that they were all the same person.
After The Doctor has taken the horse from the carriage driver, Strax rides by with his own carriage and says, "Out of the way, human scum! Hyah! Jurassic emergency"! Tyrannosaurus Rex (more commonly known as T-Rex) was from the Cretaceous period (68-66 million years ago), not the Jurassic period (164-145 million years ago).
Vastra says she uses the veil as a disguise, yet when she first sees the Dinosaur her veil is up.