Finch walks in to the lab holding the sensor for an alpha particle detector up in the air. Alpha particles can only penetrate 1-2 inches in air. The sensor needs to be in direct contact with the contaminated surface to measure properly.
Around the one minute ten second mark, Detective Fusco has dragged a body into a shallow grave. At one brief point you can see the body's cheek puff out with air. Most likely due to the actor breathing through his nose.
Dr Nelson, when his nose begins to bleed, places a napkin underneath the nostril and tilts his head back. A cardiologist (or any doctor) would not employ this outdated technique, the correct procedure is to keep the head level and apply firm pressure to the sides of the nose to stop the blood flow.