When Julius asks to come with his brother on his trip to Houston, Julius says that where he wants to go is on the way to Houston. After Julius says this, in the shot from behind him, his lips are still moving. He is saying "on the way to Houston" again.
When they are stealing the Cadillac, Julius says that if you lift the end of a vehicle to an angle greater than 45 degrees the alarms computer thinks that the car is being towed, and the alarm shuts off. 45 degrees would have to be over his head, and he lifts the car to only waist level.
Shortly after Julius arrives in Los Angeles, he tells a biker that he is from an island in the South Pacific "300 miles SSW of Fiji". In a later scene when he meets Marnie at the supermarket, he tells her that the island he is from is "300 nautical miles SSW of Fiji". A [standard] mile and a nautical mile are different measurements. A nautical mile is about 1.15 standard miles, which would make 300 nautical miles equaled to 350 standard miles.
At the beginning of the movie when Julius is on the airplane singing along loudly to the song "Yakity Yak" the flight attendant takes his headphones off and says she knew he was going to be trouble. Julius responds with "I'm sorry I've never heard this kind of music before". If he had never heard that music before, how did he know the lyrics to the song?
Julius drives Vincent's car up on the two right tires, then drops down, the car's airbag deploys. When the car falls down the camera was pulled back to a wide view from the front of the vehicle. The airbag was clearly visible for a brief moment. When the camera cuts to a close-up, there is no airbag showing.
When Julius drives the car on two wheels, the camera films Julius close up with one hand on the steering wheel and his other hand holding onto the cars front window, but in the long shots, the stunt driver has both hands on wheel.
In the opening scene the doors to the laboratory are clearly marked 'top secret' and sealed the day the twins were born, but when the twins returned to the laboratory the doors were marked 'restricted entry'.
The deal was for Beetroot to pay $5 million for the engine. At the end of the movie, the twins say the suitcase contained $4 million. - The implication is that Vincent skimmed $1 million before he returned the money.
When Julius and Vincent call into the institute to find out about their past, the car is parked over the line in the car park, effectively taking up two parking spaces. When they come back out, the car has moved down a few spaces and is parked between the lines.
When Julius is driving the Mustang for the first time and Vincent calls Julius on the cell phone to tell him to turn into the grocery store they are clearly on a busy boulevard. When Julius actually makes the turn, however, he is clearly turning off of a residential side street.
When Dr. Traven is explaining the experiment to the twins, he says that "the embryo split" to create them. First of all, embryos do not split--the zygote (fertilized egg) splits to be come two embryos. Second, if the splitting zygote was the case, Julius and Vincent would be identical twins. Obviously, they are fraternal (where two sperm fertilize two eggs at the same time).
At the end of the movie, when the chain is falling on the "bad guy", it is clearly a plastic chain as a large number of the links have the silver paint brushed off revealing the white plastic underneath.