Officer Jessop is introduced to viewers in this episode but he has been in several episodes before this, so this episode is shown out of order.
The officer died when it was pitch black, most likely the middle of the night, yet it is bright light outside when CSI shows up. Horatio tells Yelina that he left as soon as he got the call. With the death of a police officer, it shouldn't take that long for Horatio to show up to the crime scene.
Horatio Caine says, "A .22 [caliber gun] is registered to Gary Nielsen's wife." Florida law neither requires nor provides a method to register handguns. Florida does issue a "Concealed Weapon or Firearm License" which legally permits the licensee to carry a handgun concealed, but application for the license does not require divulging any information about the gun.