When Joe's wife chases him out of the 3rd Street theater, as she watches him walk away, an extra exits the building. The extra should still be visible in the background of the close-up, but he has vanished.
When Joe is helping staple the banner up, he staples his sleeve to the board. He pulls it away pulling the banner off but his sleeve is still stapled. When we cut back to Joe, he is not stapled anymore (and there hasn't been enough time for him to do anything about it).
As Meg enters STARKe Pharmaceuticals before the conference call with Mark McKinney, she walks past an extra who is leaving the building. When she gets off the elevator, she walks past the same extra on another floor.
When Callie and Natalie are walking past the karate dojo and see Joe practicing with Chuck, the front end of Joe's Chevy Lumina is visible in the shot. However, a few scenes before Joe is showing Meg his new Cadillac. Based on his conversation with Meg, it sounds like he traded in his Lumina because that was "someone else" who drove it.
Near the end when Joe meets Meg in the parking lot to confess his feelings, immediately before she gets out of the pickup, she's got her seat belt on. In the next shot, through the passenger side window, the belt is no longer on.
When Natalie and her father Joe are in the car discussing his job, a clapper board can be seen next to them between the front seats. In the next shot a newspaper is there instead. The "Joe" part of the title is visible on the clapper board.
The scene where you see Joe passing the Macaroni Grill twice on his way from home to work is geographically incorrect. It appears on the left side of the highway which means he was actually driving towards Minneapolis, his supposed home, instead of away from it. In fact, the Macaroni Grill is even more west of downtown than where his office was located so he would never be on that part of the road going to or from work at all.