Corrected entry: Many of the dead bodies in a crime scene, or cadavers during an autopsy in varied episodes are breathing.
Corrected entry: DNA results usually take weeks instead of just days like usually happens on the show.
Correction: They have the lab in-house, so they don't have to send the samples off to another lab; and they prioritise the cases by importance, so samples from the 'big' cases go first. DNA tests themselves don't take weeks, sending them off to a lab, and waiting for the lab to get around to testing them, does. Them having the lab in-house relies on suspension of disbelief, but isn't inherently a mistake.
Correction: This one is going to have to be more specific about which dead body and when as most of the time a dead body was used for the series (especially in autopsies and when they found the bodies initially); it was a prop based on a real person and thus could not be breathing as it never had life to begin with. Exceptions were when it showed a person actively dying on screen where them breathing may have been a last breath. This is going to need to be more specific to verify as a definitive mistake.