Continuity mistake: When Remy and Emile are cooking the mushroom on the roof, notice that the mushroom is skewered on the antenna. When Remy and Emile are hit by lightning and sent careening off the roof, the mushroom is instantly on a stick in Remy's hand, instead of the antenna. It could've been sent flying by the lightning bolt, but even if it was, there was no stick in the previous shot for it to have ended up on.
Continuity mistake: In the beginning of the movie when the crazy lady goes after Remy and Emile with the shotgun, she fires three shots at them: two in the wall and one towards the ceiling when Emile is crossing the banister. After Emile crosses the banister, look at the ceiling around the chandelier in the next shot. There are already 4 shotgun holes in the ceiling.
Trivia: Near the beginning of Ratatouille, when Remy is in the sewers and begins to make his way up to the skyline of Paris, he is startled by a barking dog in one of the apartments. If you pause and look at the silhouette of the dog, it greatly resembles Doug the dog, from the 2009 Disney/Pixar release Up. Obviously another precursory nod to an upcoming movie by the geniuses at Pixar.