In the scene in Ingrid Bergman's bedroom, the position of the cigar in Gary Cooper's hand changes.
Scenes set in French Quarter section of New Orleans feature winding streets (a standard studio back lot trick that saves building an entire block of buildings). In reality, all streets in the real French Quarter are at right angles to each other.
In the opening shot, Clio and her companions are on a boat in the river staring into the sunrise over the French Quarter. However, at this angle, the sun would be rising in the northwest. Additionally, buckling in the backdrop is clearly visible.