When Alice is in Dr Jonas' office and the camera is on her (and from behind Jonas), after he says "then you can judge who and what I am" you can clearly see that Jonas is still talking after the end of the sentence.
When Jerry unlocks the refrigerator, the lock is first shown in his right hand and he is turning the dial with his left hand. In the next shot, the lock is in his left hand and he is turning the dial with his right hand.
On the bus with Alice, Jerry says that the official story on Ernest Herriman is that he drowned in a swimming pool. But back earlier, when Jerry's clipping newspaper articles, if we freeze the frame and read the article about Harriman, the official story is that he was drowned in the ocean off Maryland. The dialog in the script didn't match the text on the prop.
Jerry and Alice leave the Queensboro Bridge towards Connecticut in broad daylight; a few minutes later when they cross under an interstate highway intersection in the Bronx it is pitch black dark. The two points are only about 20 min apart.
The lock on the coffee canister in the fridge has three dials on it but When Jerry offers Alice a coffee, he "recalls" that the combination is "4-23-12" which would be used on a combination lock like the one on the fridge.
When Jerry stops the car in the middle of the bridge, the view from the front angle camera shows the last car in front of them to get through was a blue Honda Civic. When the scene switches to a rear camera, it's now a red mid-size car.
Jerry and Alice get off the 72nd St. bus and enter what Jerry calls the 7th St. subway station, where Harriman drowned. However, he boards an N train in the Times Square station, with an exit to 41st St. sign visible in the background.
When Jerry leaves Alice on the train and Alice gets a phone call on her mobile phone, she is still in the subway. Mobile phone technology of the day dictates that calls can not be completed when underground in the subway. She would not have a signal to receive or make a call.
When Jerry is taped to the wheelchair and Jonas first confronts him, we see Jonas blocking the light, yet there is no shadow on Jerry. Even when we can see the back of the wheelchair, we should be able to see some part of Jonas' shadow over Jerry and/or the wheelchair.
When Jerry is driving up to his apartment in the beginning of the movie and pushes the car backwards to park on the corner, the car moves back way too easily. If the car being pushed back has an automatic transmission, the rear wheels (or the front in a front wheel drive car) would be locked, hence causing the car to skid. If the car had a manual transmission, the last driver of the car should have placed the transmission in first gear or applied the parking brake. Either way, the car would have skidded backwards. The chances of the car being left in neutral in either situation is unlikely at best, and if so, the odds of that particular car being in neutral are very high, considering the amount of cars in Manhattan.
When Jerry is trying to escape from the hospital after being handcuffed to the bed he passes through the security screen. Dr. Jonas gets caught behind the screen and demands, "Open this gate." however just before this you can see the gate is slightly ajar and Jonas pushes it closed before making his demand.
The goof item below may give away important plot points.
In the final scene in the old hospital when Alice stands over the pool and shoots Dr. Jonas who is underwater, anyone who has ever shot a pool of water knows that it makes a gigantic splash. The pool is virtually still and water is not seen flying up at Alice.