The train shown on security footage is 1996 Stock train for Jubilee line. The wagon found by Sherlock and John is 1972 Stock for Bakerloo line. And the interior for that wagon was borrowed from D78 Stock for District line.
Sherlock's tombstone appears to have changed locations between this and the series two finale. In the latter, the tombstone stands somewhat isolated, in front of a huge tree, with no more tombs around. In "The Empty Hearse", however, the tombstone stands behind the tree, in the middle of an opening, with several other tombstones around.
As Sherlock and Mary are racing to the bonfire, there is a quick sequence as they are running where Sherlock can be seen removing his coat and it's about to hit the ground. However, as they are reaching the fire, Sherlock clearly still has his coat on.
When Sherlock examines the body in the cellar (41:21) He misses the fact that this "body" is probably a skeleton robbed from a School or University. As can be clearly seen on the hand of the skeleton where individual bones of the fingers are held together with wires.
Towards the end, when Sherlock and Mary are driving to save John, a brief scene before they arrive at the police barricade clearly shows a shadow of the camera/crew on the ground.
The CCTV images of the London Underground are not the District Line . All District Line stations are twin tracks and use the larger sub-surface trains. The platform and train shown are on the deep level lines; it's most likely that the abandoned Jubilee Line platforms were used as these are still maintained for TV/film purposes.
Sherlock goes to great lengths to examine the skeleton, supposedly of Jack the Ripper in the hidden room. However, Sherlock should have spotted it was a fake immediately as the skeleton was in a sitting position, fully articulated. Without any ligature tissue to support the bones, the skeleton would be a pile of bones on the chair and floor. Molly, as a doctor, should also have known this.
When discussing the missing part of the underground-train Sherlock refers to them as 'carriages' while just moments ago they learned from the train enthusiast that they are called 'cars'. Sherlock would have integrated this information immediately after learning this (if in fact he didn't already know it before) and would not keep referring to it by the wrong name.