When Mr. Lloyd spies Ms. Brodie and the girls from his studio window, he is seen wearing dark brown trousers. He rushes from the room and when he emerges on the street, he is wearing light coloured trousers.
Miss Brodie presents a slide show to the class. She tells a tale of how Dante Alighieri fell in love with Beatrice Portinari when they met at the old bridge (Ponte Vecchio) in Florence. Miss Brodie changes some of the facts of the Dante and Beatrice story, but in doing so she is relating the story (consciously or unconsciously) of her own failed romance with an older man.
When Jenny and Sandy are toasting bread in the fireplace, they grab the ends of the forks that were in the flames. Of course, these would be too hot to touch.
The telephone on Miss McKay's desk is from the 1940s. The transmitter (what you talk into) would have been different, and the dial would have been plain black, instead of stainless steel in 1932.
Opening the scene of the girls' dance about an hour and a half into the movie is a shot of a phonograph playing a record. The record is clearly a modern (for 1969) vinyl album rather than the 78rpm records that would have existed at the time.
The very first shot of the film shows the Edinburgh skyline with a caption stating that it's 1932, but clearly visible in the centre of frame is the white cube of the (now demolished) Goldberg's department store, which was built in the early 1960s.
In the first half of the film, set in 1932, Jean Brodie speaks of Anna Pavlova in the present tense, saying "She is the prima ballerina." Sandy and Jenny's forged letter also uses the present tense when referring to Pavlova. ("I am dedicated to my girls as is Madame Pavlova.") Pavlova, however, died in 1931.
At the end when Sandy walks out of the school, she passes a 1960s-style concrete lamp post.
(at around 45 mins) In the office scene just after Miss Mackay stands up, the boom microphone's shadow is briefly visible on the wall behind her, and it moves (upper-right corner of frame).
When talking to her students about Franco, Miss Brodie says that he is referred to as "el jefe", and after pronouncing it, she adds, "The J is silent." Far from being silent, the Spanish J is a very noticeable /x/(voiceless velar fricative), like the "ch" in Scottish English "Loch" or German "Buch", or the G in Dutch "goed".
The Headmistress says that 1930 is the start of a new decade. There being no year 0, decades start with years ending in "1", such as 1931.