When Neal wakes up in the hospital, after delivering the package, he finds a playing card in a flower arrangement. As he looks at the face of the playing card, the back is clearly visible to the camera right-side-up. When he flips the card over to view the back, the back appears right-side-up to him, instead of correctly up-side-down.
During the first car scenes on the I60, especially the ones where Laura is sitting on the passengers seat, you can more then clearly see a crew member sitting next to the car door on the passengers side just "riding along". This is so obvious that it gets pretty annoying since it happens a couple of times. In one scene you can even see him wear a red scarf.
Seconds after Neal wakes up in the hospital after being knocked cold, clearly disoriented and unsure where he is, his sister comes in. He tells her the doctors want to "keep me overnight, to log some tests in the morning." How does he know this?
The goof item below may give away important plot points.
Neal's car is a BMW e36 3-series convertible. When you see the burned-out car wreck near the end of the film, it is clearly visible that it is a e30, the older 3-series model. The wreck has no damages from the impact either.