At the very beginning, they show a castle during the credits, then "In Edinburgh In 1831-" then show a closer up of the same castle and a horse and carriage, and you can clearly see two or three automobiles parked next to the castle.
When Gray kills Joseph, the latter's right arm is stretched out from his shoulder at a 90 degree angle and Gray reaches over to shoo away his cat who begins to nuzzle Joseph's right hand. In the next shot, the right arm of the dead Joseph has suddenly moved to a position where it lies parallel to his body.
The scene in the pub right after it's announced that MacFarlane sold Gray's horse and buggy for a mere four pounds and the new owner is embarrassed into buying him a drink. Right after the barmaid goes to fetch him one, Fettes enters the pub to talk to the Doctor. When the barmaid returns, she has two drinks. Yet she had no indication that MacFarlane was meeting anyone, and the doctor didn't know Fettes was looking for him.