The "new" can-can dance routine from Paris mentioned in a theatre brochure had been around since the 1840s and, as the film is set in 1888/89, the dance was hardly "new". When it comes to the actual dance they perform, it is the French can-can, a style that was not made popular until the 1920s.
As Inspector Warwick has a thumbprint left by Jack the Ripper at the scene of the final murder, he asks that something held by the chief suspect "Slade" be obtained. Since the Ripper murders occurred in 1888/89, this is three years before the first recorded case of a murderer being caught through fingerprint analysis--in Buenos Aires, Argentina, in 1892, when Inspector Eduardo Alvarez made the first criminal fingerprint identification. He was able to identify Francisca Rojas, a woman who murdered her two sons and cut her own throat in an attempt to place blame on another. Her bloody print was left on a door post, proving her identity as the murderer.
Much is made of anyone with a black leather bag or satchel falling under suspicion as the Ripper. In reality, anyone seen wearing a leather apron in the fall of 1888 in London was suspected of being the Ripper.
When Inspector Warwick is showing Slade and Lily around Scotland Yard's "Black Museum", he shows the death mask of a man who was "publicly hanged outside Newgate Prison six months ago", but the last public execution in England was in 1868 whilst the film is set in 1888.
The card that accompanied Inspector Warwick's flowers had the word "theatre" (British spelling) spelled as "theater" (American spelling). Victorian London did not spell any words in the American style, let alone "theatre".
It is obvious during the horse and carriage scene that it is a stuntman, not Palance, participating.
The Thames River as seen in the film is obviously a studio tank. It has no current, and when the police enter it to find Slade's body at the conclusion, the depth doesn't rise above their thighs.
In the opening and closing shots which include London Bridge at night, anachronistic cars and buses clearly can be seen crossing the Thames.
After Lily's opening performance, Inspector Warwick interviews her and tells her that a man carrying a small black bag was seen in the vicinity. This interview involved ONLY Lily, and NO one else was present. Yet a moment later, as the Harley's were going to bed, Mrs. Harley said that "the man from Scottland Yard said that the Ripper was carrying a little black bag." As Mrs. Harley was not present when he told this to Lily, there was no way for her to know this unless she read it in the script.