When Olivia and Noah are in the park and Olivia's phone rings, her jacket is off. On the second ring, however, her jacket is back on. She wouldn't have had time to put her jacket on in between rings.
During the scene in the playground sandpit, the amount of sand in one of the plastic toys increases between shots even though no one touches the toy.
The pistol the little boy in the park had is a Glock, however the gun pictured on the evidence board that is supposed to be the same Glock the kid has is not the same gun. The photo appears to be a Springfield XD.
When Rafael Barba answers questions from a crowd of journalists, several of the handheld digital voice recorders that are supposed to be recording his comments are not actually turned on.
Olivia throws away her coffee cup and it lands on a newspaper highlighting the death of Sgt. Dodds. The death was weeks prior to this scene, as Olivia has already been to Paris and back, so it is very unlikely that there would be a crisp, weeks-old newspaper lying on top of a trashcan in a popular area of Central Park.