When Sam and Jake are in the "acting Class" Sam stands up to stop the "teacher" from picking on Jake. Sam picks up his gear bag and they go towards the door, but a few seconds before, the row of chairs that are in front of Sam didn't have anything on them.
When Gloria is looking in the window at Bellini's, the woman walking past in the gray and black suit and hat appears to back up and start over from the same spot in each frame.
When Jake discovers Carol cheating on him, her lover's left hand is on her right breast. When the camera switches to a close-up, his right hand is on her left breast.
In the dressing room, the saleswoman pulls a curtain partly closed. In the next shot, the curtains are in their original position until Gloria Revell herself closes them further.
After Jake is attacked by the white dog that belonged to Gloria, he is shown with a big blood stain on his shirt and a bandage on the left side of his neck. The following day/days later, there is no sign of an injury or bandage on his neck.
The Indian had used an auger bit to open the victim's safe, and eventually to kill her. An auger bit was used because of its aggressive look, but would have no effect on a steel safe. They are for wood.
The first time Jake spots Gloria through the telescope he watches her for a moment, then she moves across the room. Jake is then shown turning the telescope a couple of inches to follow her movement. From his distance, a couple inches would have been much too far too keep her view.
The police are in the habit of looking at the spouse of murdered individuals and would've immediately been able to discover Sam was not in Seattle as he claimed and that a call was placed to Jake from Gloria's phone from Sam, who said he was still in Seattle. De Palma expects us to believe the police are incompetent and only Jake could solve this mystery.
When he's recounting to Sam about finding his girlfriend Carol cheating on him, Jake says he saw her "lying there." But per the editing of the scene, Carol was sitting on top of the man she was having sex with, and if she was lying down he wouldn't have seen her the way it was shown in the film.
When Jake is being interrogated by the detective, the detective initially says that he has a problem with Jake because Jake is the only witness to the murder. Later in the interrogation, the detective says that he can not hold Jake because he has witnesses to back up Jake's story.
The first time "The Indian" attempts to use the drill, when the cord is too short to reach, the drill is running in reverse. That would make it pretty tough to use in the eventual manner.