When Sophie is in Victor's restaurant kitchen to announce her going back to Verona, Victor sends all the kitchen employees out of the kitchen. While the employees are there, there are cooking sounds. After the employees are gone, the cooking sounds are gone but all the cooking is still happening in the background.
Charlie is Claire's grandson, the son of her son, but his last name is different than hers. If she was only married once, per the plot, then her current last name should also be her son's and her grandson's. (Or am I missing something?)
When Sophie first visits the Juliet Secretaries' office, she and Isabella look out the window down at the street where they see women walking into Juliet's garden. In this shot the window blinds are tilted downward, which allows them to look down from the second story to the street. A moment later the scene changes to Sophie and Isabella talking, and the blinds are now tilted upward, which would block the view to the street below.
When Charlie arrives in Verona to meet Sophie, the car turns right and stops on the left side of the street. However, seconds later the car is parked on the right side when he opens the door and exits the car.
When Sophie first walks into the area with Juliet's wall, you can see a man taking a picture walking with his family over her left shoulder. The camera cuts to show the wall and then back to Sophie, where the man once again appears walking behind, taking a picture.
When driving around Italy, looking for Lorenzo, they are alternately shown driving on the left and right sides of the road. In Italy they drive on the right side of the road. This may be due to some frames being flipped (left-to-right).
When Claire is walking towards Lorenzo the first time they meet in the vineyard, shots of Claire show the sun coming from her right in the late afternoon, but shots of Lorenzo show the sun coming from HIS right (what would be her left), and nearer the middle of the day.