The hat Gus finds in the basement and calls Rose-Marie's looks nothing like the one she's actually seen wearing while watching Ed act.
Gus claims that the doctor-patient confidentiality agreement is moot when you're suspected of murder, but the California Evidence Code (Division 8, Chapter 4, Article 7) does not provide any such exception to psychotherapist-patient privilege.
At the crime scene, a man is found to have committed suicide by hanging yet his feet are much too high to have jumped off the overturned chair. However, he is hanging above the table, so he apparently put the chair on the table and then stood on the back of the chair to hang himself.
When Gus turns the corner in the picket-fence room, the camera's shadow on the right-side wall moves when the camera pushes in on the doorway.