As Marilla is coming upstairs Anne is lying on the bed with her hair loose, when Marilla finds the missing broach and calls Anne she comes out with her hair in braids.
When Anne is being shown how to milk a cow, the cow clearly has an ear tag, with a serial number. Cattle tagging wasn't introduced into the Canadian agriculture system until 1998, becoming compulsory in the early 2000s.
Anne's freckles go from blatantly obvious to barely there to nonexistent and then back to blatantly obvious again.
At the Christmas concert there are three candles on the stove, as it was Christmas the stove would be very hot and the candles would melt.
The story is set in the 1880s during the Victorian era, but the teacher had them sing God Save the King. King Edward did not succeed until 1902.