Katie calls and leaves a message on her neighbor's answering machine while at work at Ivan's on a Monday (according to the answering machine). When Kevin calls Ivan's and listens to the recording, it states that Ivan's is open Tuesday to Sunday, meaning it is closed on Monday.
When Kevin Tierney drives away from the 4th of July Parade roadblock, the car has a front license plate as it begins to turn around. In the next shot of the front of the car there is no front license plate.
After Katie and Alex get caught in the rain storm and go into the restaurant, Katie's face is instantly dry and her makeup hasn't been affected at all. Her hair appears to be freshly combed as well and looks dramatically different from when they first walked in the door.
When Katie arrives in Southport, the bus number is 199. You will see this when she turns to see the bus is leaving. It is also shown on the top right at the back of the bus as it pulls away from the gas station.
When Gavin reviews the security footage and believes he recognizes her, the bus number is listed as 1994.
The "Atlanta" bus number keeps changing. When first seen, it is a four digit number. When Katie gets off in Southport, it is bus number 169. And when Kevin sees it on the security camera tapes, it is a four digit number, and although we can only see the bottoms of the digits, the last two are "55".
When Tierney talks to the bus station clerk about where you can go from Atlanta, a blonde woman walks to the left of them, in the next shot she walks the same way again as if she has never walked by them before.
Near the beginning of the film, an aerial view of the bus taking Katie to Atlanta is shown traveling on the Linn Cove viaduct in western North Carolina. The Linn Cove viaduct is part of the National Park Service's Blue Ridge Parkway and is closed to commercial vehicles including buses.
Kevin travels to Southport to locate Katie in an unmarked police car - note the police license plate, radio antenna and grille lights. Earlier he had been suspended from duty, with his badge and gun being seized. There is no way he would have been able to keep a departmental vehicle, and no way he could have simply taken off with one from the station without anyone noticing nor trying to stop him.
The goof items below may give away important plot points.
During Katie's flashback, she clearly take both pie plates and the wine bottle to the kitchen, but only brings the wine bottle back to the dining room table. However the pie plates are clearly seen on the kitchen table when the husband returns home later in the movie.