When the Judge asked for the counselors to approach her desk (in the courtroom,) her hand is shown off her microphone when the camera is not towards her, but when it is her hand is covering the microphone so no one can hear her. It happens so quickly that it is impossible for a human to actually do it in that much time.
In the opening breakfast scene, when Josh gets up from the table to go to school he leaves his two plates of eggs and toast on the table. In the next shot he is leaving with his sister and the plates are now magically on the kitchen counter.
After the dog bites Dave Douglas, it is taken away to the shelter to be tested for rabies. The standard test for rabies (and the only one that could return such rapid results) is the direct fluorescent antibody test, which is performed on a sample of the animal's brain tissue. Typically, the animal's brain or entire head is removed and sent to a lab for testing.
When Dave is distracted driving to the courthouse, he slams on the brakes and the car slides to a stop. The age of car that he is driving would undoubtedly feature ABS (Anti-lock brakes) and therefore would unlikely slide in this manner.