During Sara's party, Ms. Minchin is called away. The scene cuts to her in her office then back to the party where Sara is blowing out her candles. While she is making her wish, we can see Ms. Minchin walking away in the back.
On the letter Sara receives from her father, it has her name spelled with an "H" at the end ("Sarah"), but on her birthday cake her name is correct.
Miss Minchin follows a maid out of the birthday party room and meets with a lawyer in her office. But in the next scene, both Miss Minchin and the maid are shown still leaving the party room as Sara blows out her birthday candles.
In opening scene, the father is referred to as "Captain" which is correct because the movie takes place in 1899. After 1902 until the present (2018), the rank on his shoulder is that of first lieutenant based on the two pips he wears. A captain's rank is three pips.
There are many references in the film to receiving "mail" and "mailing" letters. The British terminology is always receiving "post" and "posting" letters.