When Dr. Flemming returns to argue with his wife at 1 AM, Los Angeles appears from their balcony in the light of dusk, the same lighting that appears in another scene (actually set at dusk). Another reviewer points out that you can see a shadow on that LA backdrop in a scene.
When Joan Hudson is under observation from outside her apartment, her silhouette is visible on the curtains as she moves about. She is clearly visible from top to toe. When the scene moves inside the apartment, the shadow of her lower half is completely obscured by a large sofa and a table.
When Dr Flemming and Joan Hudson leave his apartment for the airport, the telephone receiver is on the cocktail bar. When Dr Flemming returns to what is now a crime scene, and therefore nothing should have been moved, the telephone has moved to a table in the middle of the room.
The reception room at Dr. Fleming's office features a distinctive painting of trees and white houses with red roofs, which is prominent in several scenes. This same painting later appears in Columbo: Suitable for Framing, as part of the art collection sliced and stolen by Dale Kingston. In its return appearance, this painting is also part of a goof because it magically mends itself and returns to the wall, after it was vandalized and removed.
(at around 1h 16 mins) When Columbo steps back into Dr. Flemming's office to turn off the lights, the switch is already in the down position. He simply touches it without moving it, and the lights turn off.
When Dr Flemming is strangling his wife, he is directly behind her, the top of her head at his eye level and her hair almost touching his face. But in the closeups of his face during the struggle she isn't in the shot.