When Michelle Pfeiffer is in the taxi with George Clooney's phone, he calls her up to give her messages. She then acts totally surprised that they mixed up their cell phones and she has his, but then continues to say he has a meeting at 4, indicating she already knew she had his phone by mistake because she took a phone call for him.
When Jack crosses the street with the two kids, a tracking shot shows the sign reads "DON'T WALK." Then the view switches to in front of them and the sign on the opposite side of the street says "WALK."
When Melanie and the kids are sitting eating their ice creams, a large clock can be seen on the wall. It appears to read 6 o'clock, when the time should be around 3:30. (even if it doesn't say 6, it most certainly doesn't show anything remotely close to 3:30).
Near the end of the movie, when the kids are watching "The Wizard of Oz", they want to fast forward past the Ms. Gulch taking Toto to the county sheriff part. When Melanie fast forwards "to the color part", the music heard is clearly NOT from the color part, but rather from when Toto returns to Dorothy from escaping Ms. Gulch's basket. There is also no way it took Melanie almost the entire movie to get ready to spend time with Jack, but we hear the end of the "Wizard of Oz," in order to end the movie.
When Melanie and the children are at Serendipity, she tells them to switch desserts. When Sammy begins to push his Frozen Hot Chocolate to Melanie, the ice cream is exactly even with the top of the bowl. In the next shot, we see him push it directly onto Melanie's jacket and it gets all over her. At this point, the ice cream is well above the top of the bowl.
The plastic wrap on the fishbowl changes between shots. When Melanie first leaves her apartment to go to Maggie's there is no wrap on it. When she's on the street and arrives at school it is covered with wrap and a rubber band. Maggie removes the wrap at "breakfast" and it remains uncovered when Jack takes it to his office.
After the soccer game, it's evening when Jack puts Maggie to bed, and dark when he gets her out of bed and goes to the fish shop, but then when they're at Melanie's apartment, it alternates from a rainy night to sunlit day out the window.