Early in the film, as Phyllis finds Walter's address in the phone book and goes to his apartment, Neff turns on a three-way lamp by the door using a switch on the wall. Later in the film, the lamp is gone.
After Neff meets with the President of his company, he returns to his apartment and places a folder on the chair to the right of the door. When Keyes comes to the door, after Neff's brief phone conversation, the folder is nowhere to be seen.
The door to Neff's apartment opens away from, rather than toward, the apartment. This was a violation of the Los Angeles Fire Code. (Billy Wilder knew this, but could not change the door because of the crucial scene where Phyllis is hiding behind the door in the hallway.)
When Keyes approaches to speak to Neff as Neff enters work one morning, Neff asks Keyes if it has to do with the "Peterson" case. The name of the character in question is "Dietrichson," not "Peterson". However, this could be seen as Neff's try to show no interest to the case.
When Dietrichson's body is discovered on the tracks, and presumed to be the victim of an accident, his body would have been taken to the medical examiner's office for identification and autopsy. It would have been quickly discovered that he had been strangled, and had not fallen from the train due to the absence of bruises on the body.