Factual error: Though the movie is playing with historical events for "laughs," it should at least be pointed out for the record that Queen Victoria died in 1901, and the Titanic didn't launch until 1912 (and its construction didn't even start until 1909). So, obviously, there's no way Victoria could have toured it before its maiden voyage. (And the movie acknowledges that it's supposed to be THE Titanic since it shows Moriarty reading a newspaper reporting that it sank, to say nothing of the Billy Zane cameo).
Factual error: Some of the newspapers have the wrong date. During the opening, the article about young Sherlock is dated "Wednesday, November 24, 1870." However that was a Tuesday. Later, the article about the killer on the loose is dated "Friday, December 15, 1892." However, that was a Thursday.
Audio problem: On the Titanic, whilst Mrs. Hudson is tying Watson to the cogs, she says "I'll be on my way to America by the time the bomb explodes" shortly before she leaves him, but the movements of her lips do not match up with the dialogue heard coming out of her mouth, revealing that the line was poorly dubbed over.