In the movie, Adele notes that her name means "justice" in Arabic. However, Adele does not have Arabic origins, but rather Germanic origins. There is an Arabic name "Adel", which does mean justice (and does not have a female equivalent) which may have led to the confusion.
When Adèle dresses up for Emma's vernissage, we see her painting her toe and finger nails red. In the next scene we see her walking to the vernissage, and when she adjusts her hair, her finger nails are not polished.
When Adele first sees Emma on the zebra crossing, she is heading to the prefecture of Lille but in the next scene she can be seen at the great square. This is impossible as the square is in the direction she is coming from when she sees Emma.
When Adéle goes to Emma's art gallery opening, there's a dolly shot of her walking from left to right towards the entrance. There's a reflection of the top of the camera in one of the windows of the building.
In one of the classroom scenes when Adele is walking down an aisle of desks there is a bump from the mic pack in the bottom of the back. In the next shot there is a glimpse of the mic pack moved to her left hip.