When you first see Mr. Walbridge in the boardroom with his team, the conference room appears to be as high as the 40th floor, yet you can hear street traffic as if it was at street level. Also, the windows are ceiling to floor and don't open, so there would be no street noise. The boardroom was actually a set built on a sound stage at Sony Culver Studios, any traffic noise was added in post production as a sound effect, mistakenly or otherwise.
(at around 30 mins) When Zohan paralyzes the child in the barber chair by pinching his shoulder, the child falls forward with his hands in his lap. Moments later, the comatose child is shown with his hands cushioning his face.
(at around 1h 15 mins) When Salim calls The Phantom to tell him about the Zohan being in US, he dials a very long phone number using a regular wireless telephone, yet he sends a picture using a cell phone.
(at around 45 mins) When Zohan is allowed to shampoo the hair of Mrs. Skitzer, he initially lays her back and visibly moves her long hair into the washing sink. In the very next cut, her hair is outside of the sink again. Then when he pulls the purple cover up over her body, her hair is again back inside the sink.
(at around 10 mins) When Zohan and Phantom are fighting in the water outside of the Lebanon stronghold, Phantom grabs a Piranha out of the water and lets it bite his neck. Not only are Piranha only native to South American rivers, but are also freshwater fish. The water in this scene would have most likely been the Mediterranean Sea, which is saltwater.
The headband of the Phantom has the word Phantom written on it in Arabic. In the early scenes, the letters are not connected, whereas later on they are. (All Arabic words when written are connected - if not it is just a collection of letters that mean nothing.)
Israel plays Lebanon in the hacky sack tournament, yet the Israeli flag is shown with the Palestinian flag. There is actually a mix of Palestinian and Lebanese (cedar tree) flags in the crowd, large numbers of Palestinians still live in refugee camps in Lebanon and would support any team playing against Israel.
The goof item below may give away important plot points.
When Zohan and Phantom join together to fight against the fake Arabs in the street, Zohan is wearing jeans and Phantom is wearing red pants. As Phantom is measuring Zohan's right foot, another fake Arab approaches Zohan. He kicks him with his left foot, which is wearing khaki shorts.