Continuity mistake: In the first classroom scene, Miss Brodie is talking to her students. She approaches her desk, places her hands on her desk and turns around, all the while talking and keeping her hands on her desk. In the next shot her hands are off her desk, folded.
Continuity mistake: The windows in Miss Brody's classroom seem to have minds of their own. The one she admonishes a student to lower to six inches closes itself completely a few shots later. Another, in a later scene, reduces the amount it is open by several inches between takes.
As director Ronald Neame himself points out in his commentary to the DVD, immediately after Sandy has been heating a piece of bread in the fireplace, she grabs the end of the fork on which it is placed and does not burn herself.