When Claire is flirting with Junior and orders dessert, there is an advertisement for Dad's Root Beer on the wall behind her; the word "beer" is marked out. Then when she flirts with a customer, the sign is not marked Also, the salt shaker, absent from the first shot, appears on the counter in the latter shot; other condiment containers on the counter also are in different positions.
Near the end, Warren Quimby puts both his hands in his pockets while facing the camera and talking. Then, in a reverse shot from behind, he is seen with his hands out of his pockets and putting them in again.
Deager smashes Claire's doll after Paul leaves. Later, when she is unpacking back home, she picks up an unbroken doll from her suitcase.
When Warren and Claire are being questioned by the police, Claire's right arm alternates between at her side and on Warren's shoulder.
The policeman at the beginning says that the first word of the Homicide Department is "a fancy name for murder". In fact, Homicide investigates all suspicious deaths, a few of which turn out to be murder but most of which are manslaughter, accident, or suicide.
The exterior of the street outside drugstore (shot on actual location) does not match with views of same street as seen through window of drugstore interior (a set).
In the beach fight scene, the ocean is not level. A cameraman's objective is to level the equipment, particularly when the horizon is such a prominent element, as it is when dealing with water. Here, it's 0.69 to 2.0394 degrees off level, depending on whether the shot is along the beach or straight out to sea. (The solo shot of Claire is the worst.)
Lt. Gonsales enumerates the various reasons why Paul Sothern was an alias including the failure to find any rental or residence listed under his name. Since he had rented his room, though, there likely would have been some record of it, and with some "legwork", the police might have determined that a person by that name, alias or not, did exist.
After Bonnabel tells Claire that all the furniture and furnishings in the apartment had just been changed, leading her to believe that the hidden gun she has just uncovered had to have been planted by her afterwards, she readily accepts the change of furniture story. She never questions why the furniture would have been replaced at all, questioning Bonnabel's story - which, as it turns out, was a ruse, anyway, and simply allowed herself to be placed under arrest and to be led away. without protest or question.
Once the existence of Warren Quimby and Paul Sothern had become known to the police, and even before it was established they were the same person, a comparison of their fingerprints would have confirmed that they were, in fact, one person. Their fingerprints might have been taken directly from them or might have been lifted from objects they handled, but the use of fingerprint comparison never arose.
Near the end of the film, Lt. Bonnabel signals to Claire to go and check a chair where the gun might be hidden. She feels under the pillow, finds the gun, and lifts it out, giving it to the police. Surprisingly, she doesn't question the way she was allowed to pick up the gun and putting her fingerprints on it, even though she'd used a handkerchief when placing it there shortly before. She should have questioned that she was allowed to handle it at all. Something was obviously fishy here, but she dismissed it, without a thought.
When Claire retrieves the gun from behind the rock, she's careful to use a handkerchief to hold it. This makes no sense because her fingerprints already were on the gun and trigger after she shot Barney, not Warren's, whom she wanted to falsely implicate. It's as if she were trying to preserve evidence that would convict her.