In the scene where Vianne jumps off the dock into the lake, you can see Vianne jumping and Roux watching her from behind with a calm expression. When the camera switches to Roux's close-up, Roux's back is to the camera. He then turns around and looks shocked for a second, then says "Jesus..." and jumps in after her.
When Roux enters Serge's shop at first with the little girl, it films her hair, which is neat, straight and glossy. Yet when Serge says he doesn't "serve animals", it films the girl again, and suddenly her hair is totally messed up and tangled.
Early in film when Vianne makes Amande her first cup of chocolate, she fills the cup only half full of chocolate. Then she adds the chili pepper and the whipped cream. When she places the cup of hot chocolate in front of Amande, the cup is very full.
When Vianne and Anouk first meet Roux at the dock, it is an overcast day. Yet while Vianne and Anouk are shot in the "overcast" light, Roux is shot with a light on his left side, as if the sun was setting.
When Vianne and Anouk first come down to see the River People, we hear Roux playing a guitar, but can't actually see him. Then, when the two finally see Roux, he's sitting right ahead of them, in front of a white screen, where no one was sitting the shot before, playing a guitar.
When Vianne takes the newspaper down from the shop window on the day it opens, the shots from the inside show the window covered in dust and cobwebs, while from the outside the window is clean and shining.
When Roux enters the chocolate shop the first time, Vianne hands him a chocolate to try. As he is eating the first bite, the camera changes angles and we see that the chocolate has been completely eaten.
When Vianne and Roux are in the river, the two change (between shots) from Vianne facing away from shore with Roux's arm across her chest to Vianne facing towards the shore with Roux's arm around her shoulders.
The goof items below may give away important plot points.
When Vianne offers Comte Paul de Reynaud the glass of refreshment (after he has destroyed the window's display, and then awakens) the first glass she offers him is larger than the glass is moments later.