Goofs

When Philo Vance opens the closet door, a dead Brisbane Coe falls out, and his hat rolls away from his head. But on the closeup shot of the dead body immediately after, the hat is back on Brisbane's head. Then on the next shot, which is of Brisbane and the servant, the hat is once again off his head.

When Gilley is killed, it is raining, but Hilda's hair and clothes remain dry. Sir Thomas McDonald's hat is wet when making the phone call to Brisbane.

The desk Sergeant taking the call at the station house about Archer Coe is wearing stripes, but has a patrolman's badge on. The Sergeant's badge is a different shape and larger.

When Vance is first talking to the coroner, he refers to the "suicide" weapon as a revolver. In fact, it's a 1903 Colt Pocket Hammerless, in .32 caliber. It's a semi-automatic pistol, nickel-plated with a pearl, or mother of pearl, grip. The Colt medallion is visible at the top or the grip when it's shown in Coe's right hand. Humphrey Bogart frequently carried a blued version in his detective films.

It's never explained where Philo gets the detailed models of the buildings involved in his explanation of this theory of the crime.

There's no requirement to explain every detail in a film; things happen off screen, and making models is relatively trivial.

When Philo tells the D.A. to release the suspects, he puts the accent on the second syllable. The first syllable is accented when the word suspect is a noun.

While that is the typical pronunciation, people often mispronounce words. In this case, it's actually an affectation that William Powell continued to do throughout the The Thin Man (1934) series.

The police break down the door to get to the body in the study. The next day Philo demonstrates how the door was locked from the outside after the murder, but the door shows no signs of being broken, and it is unrealistic to expect it to be fixed so quickly.

(at around 12 mins) The boom mic can be seen reflected in a mirror in Miss Delafield's apartment.

When Philo is retelling his reenacted version of the crime, he says Brisbane removed the revolver from the drawer, then he pointed the revolver and shot Archer. All good except for the fact it was not a revolver; it was an automatic pistol. A revolver has a round cylinder that holds the bullets, and revolves as it is fired.