When the lady falls off the horse, a red-suited servant holds one horse while Holmes holds the other, yet when Milverton passes by in his carriage, Holmes is seen holding both horses by himself.
The opening credits state that the story is "based on Sir Arthur Conan Doyle's 'Charles Augustas Milverton'". This is a misprint for "Augustus".
A Scotland Yard police detective is seen picking up a discarded weapon with a handkerchief which was not a common practice in 1894, when the film was set. Fingerprint detection was not adopted in Britain until 1901, if that was his reason. Actually, the gun was covered in blood and the policeman would seem to desire keeping his hands clean of blood.
The typeface used on Milverton's card which Holmes receives from Colonel Dorking is Goudy Oldstyle, which was originally created by Frederic W. Goudy for American Type Founders in 1915; the story takes place in 1894.
At time 1:26:03 there's a crew member holding what looks to be boom mic behind the party guests dancing. He is clearly wearing a modern white polo shirt.
When the maid comes into Milverton's study, she says, "I'm here to light the fire." A housemaid or scullery maid would never speak to the master of the house without being spoken to first. And when he tells her not to light the fire and just to leave, she replies, "Oh. Okay." Most likely she would not say anything, or might say, "Yes, sir." But she would never say "okay" (which is probably anachronistic in British speech in any case).