While having ice-cream in the diner with Melanie, the kids' ice-creams turn abruptly in every shot. Watch the position of the banana.
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.
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."
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.
On the way to the soccer game, Jack is holding Melanie and stomping in the puddles. His pants are wet and discolored to above his knees. Yet when they arrive at the soccer game (assume within minutes) and Maggie hands him her back pack to hold, his pants are dry and there is no discoloration.
Towards the end of Melanie's split screen call with Sammy at the day care center, Maggie (situated behind Sammy) seems to morph.
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.