Towards the end of the film when Dave receives the short letter from Balthazar, he is wearing his dragon ring, however his dragon ring was taken earlier and he is not wearing it before or after the letter.
When the film indicates that it is "Ten Years Later, To The Day" before showing Dave as an adult, it is understood that it is the year the film was released; 2010. Therefore, the events of his childhood encounter at the Arcana Cabana would be anytime in the year 2000. However, in the shot of his school bus on the bridge that shows the downtown New York skyline, the twin towers of the World Trade Center are not there.
When Balthazar (Nicolas Cage) is tied to the circular electric device in the lab, the two lines that tie his left hand to it are either close together, crossing over, or far apart, depending on the angle of the scene used.
In Chinatown after Dave has ran away Balthazar is turning his head and looking around the room. The man-doll in the left is without acupuncture needles and Balthazar's right hand is stud with it. In the next shot the doll is full with needles and Balthazar's coat without any.
When Dave listens to the radio while playing with his "Musical lightning" project, he is clearly standing in a Faraday Cage so to prevent any electric shock. This kind of equipment is also supposed to block any radio signal, which means that his radio would not be able to work as clearly as we can hear.
When Balthazar (Nicolas Cage) is released from the urn, he is not wearing a hat. In the next scene, he is wearing a hat. But if a sorcerer can change his appearance at will, and change the model of his car in one touch, surely conjuring a hat from the thin air wouldn't be too difficult.
In the car chase sequence, Balthazar's car is a right hand drive car. In the deleted scenes it shows Balthazar and Dave switching seats in the car. This way when Balthazar changes the car to the left hand drive he will be in the driver's seat again.
Dave playing the songs on the Tesla Coils is actually impossible, but he actually stated that he was only trying to generate plasma, not that they were plasma coils. Therefore, the music played by the Tesla Coils can be justified.
When trying to explain to Dave the difference between sorcerers and humans, Balthazar says that humans use only ten percent of their brains. This is a popular urban legend, and is completely false. But Balthazar only asks, "You've heard that humans only use 10% of their brains?" He NOT stating that error, he's merely asking David if he's heard of it.