Marcus hands the gun Sherlock found to a CSI who promptly bags it, this is totally improper procedure, a CSI would never bag a firearm without removing the magazine and clearing the chamber to make sure it isn't loaded.
The person Holmes eventually identifies as the murderer is not physically capable of ramming a fireplace poker through an adult human body rapidly enough to capture that body in a standing position against a wall. Not even a large spear gun could do it.
The sheet-rock wall is not strong enough to support the weight of an adult man on the edge of a fireplace poker shaft. The poker would tear down through the wall at least until the knees hit the floor.
Julius explains that near-earth asteroids are sized by their infra-red (heat) emissions. But any object close enough to Earth to be a threat is obviously in a ballistic orbit, whose mechanics reveal each object's true mass, regardless of its temperature, reflectivity, composition, or emissivity. Newton's original theory of gravity was based on observing comets' orbits (not an apple falling).
When examining the semi-automatic handgun at the crime scene, Holmes observes the magazine was not seated, and that it would not fire. This is likely incorrect. Presuming a round was chambered and the gun did not have a magazine safety, the handgun would fire, however, it would not properly reload without the magazine being fully seated. The gun may also have had the safety bypassed, something an external examination could not determine. He makes a second error in using the handgun as the basis for premeditation. The ownership of the handgun had not been determined. The handgun may have belonged to the victim. It would be illogical for a killer to leave their handgun at a crime scene.
Holmes mentions the "toxins" in poison ivy oil. There are none - the oil is hyper-allergenic to most (~80%) people. He should also know that a strong dose of antihistamines is a much more effective remedy for the allergic reaction than anything smeared on the surface of the skin.