The telescope on Mannix's desk changes position when Brett Nichols enters his office. When she first enters the office the telescope is level. Then it's pointed almost directly at the ceiling when the camera is on Ms. Nichols and switches to raised about 45 degrees when the camera is on Mannix.
When Mannix is reading Brett's apparent confession to the murders it ends with her saying that he should not frame the letter. This is a reference to earlier, when he saw Brett's application letter for work in a picture frame. This line essentially "proved" that she wrote the confession. But it is subsequently revealed that someone else is the actual murderer and that the confession is a fake, written by the real killer trying to pin the killings on her. But in that case, the real killer could not have possibly known to use the "don't frame this letter" line because only Brett and Mannix knew it.
When Mannix finds Brett in her bed he calls for help on the phone. He is heard dialing four numbers on the phone. Most people then would have simply dialed the operator and asked for an ambulance. The then new 9-1-1 service was in the process of being rolled out, but it doesn't explain why he dialed four numbers instead of just three.