The society papers seen when Enola and Tewksbury meet in the garden still list Tewksbury under his former courtesy title of Viscount, when he should be addressed by his current title of Marquess, a position he has held since the death of his father in the first film.
The sheet music that Enola gives Sherlock doesn't match the one she got from Mae or the one that is used to find the stolen list of names at the end. The musical notes match, but not the additional markings around the notes and the position of the 'X'.
Possibly deliberate by film makers. At 1hr 53mins Lord McIntyre uses a foot-light candle to set fire to the evidence. As the theatre was closed and footlights are only needed during performances, none of the candles would have been lit.
At the ball, Enola dances "The last waltz of the night" with William. However, the music that's playing is not a waltz. A Waltz is always in 3/4 time, but the music playing during the dance is in 4/4 time.
Prop knives in theatre and movies are usually dagger-style knives as the blade retracts under spring tension into the hilt or handle. A switchblade knife springs from a folded position into an open position around a pivoting pin. It cannot physically retract in the way shown.
The handwritten love note that is a crucial clue is an obviously rasterized color laser printout in closeups, yellow "Machine Identification Code" dots included.
After waking up from his stupor, Sherlock tells Enola that her neck is red, speculating that someone held a knife against it. A look at her neck in the next shot of Enola shows that her neck is not red and there is no indication of a knife being held to it.
The music paper has a 3/4 time signature or waltz timing thus they are suppose to be 3 beats in each measure. However some of the measures have a whole note which is equal to 4 beats therefore making some measures more than 3 beats.
Bessie tells Enola that her sister worked a second job washing glasses in a pub. In fact glasses were not used in pubs until around the end of World War One. Instead, beer was served in either a china pot with a strap handle or a pewter tankard.
Bank accounts did not have numbers until the 20th century.
Fingerprinting was not used by UK police until after 1890. Although it is described as a new discovery in the movie it is still a few years early.
Enola Holmes has shaved armpits.
When Enola helps Sherlock up the stairs, she says, "Lift your right leg," but her lips don't move.
The script mostly succeeds in making the dialogue period-specific, but at one point Tewkesbury says to Enola, "I wrote you". This is an Americanism; an Englishman, even a modern one, would have said, "I wrote to you".
In the carriage scene with Enola and her mother. Enola throws the bomb out of the right side of the carriage, but the police are on the left side throughout the scene.
A gentleman at the balcony speaks to his friend and raises his eyebrows in a very modern way of acknowledgment.