Character mistake: Seven minutes into the show, Sarah Sidle is about to do an internal sexual assault exam/kit on an unconscious victim in the hospital, Sarah picks up a metal speculum and says aloud to the victim (in a presumed moment of empathy), that she "never really liked this part of my yearly exam. These things are always freezing" referring to the speculum in her hands. She then brings a speculum to her mouth and begins to blow open-mouthed on it two times, forcing her hot breath on it to warm it. She then begins to insert it into the victim as the scene cuts away. This is pure stupidity, as no trained CSI would ever contaminate the tool like this. Sarah just added her own DNA to the speculum via her breath so any saliva or body fluids are now on the speculum what she is about to use on this patient, who is now also exposed to any STDs from Sarah.
Blood Drops - S1-E7
Continuity mistake: At the end, when Tina is shown the photos of Brenda they are in a pile of three. The camera cuts to a long shot and there are two in a row. Cut back to Tina and they are a pile of three again. This happens on and off throughout the scene.
$35K O.B.O. - S1-E18
Continuity mistake: In one shot Grissom puts a shoe on its side with a pencil. In the next shot the shoe is upright again.
Continuity mistake: When Sara is showing Greg the route the old woman took in her car, she draws a blue line on the screen with her finger. When she says something about turning left she draws a continuous line to the "Meadows Lane," but when the shot changes and goes back the line is broken into two.
Blood Drops - S1-E7
Continuity mistake: Sara takes pictures of Brenda with an UV light camera. The camera used to film the episode for broadcast is barely able to show the walls in the background as tiled. When the UV pictures of Brenda are used in the interrogation, the photos show Brenda's back up against the tile wall.
Continuity mistake: When Brass is interrogating the bartender, there is a cup of coffee in front of him. In the next shot of the bartender's face, the cup is gone. It reappears later on in the scene in a shot from the side. (00:27:00)
Cool Change - S1-E2
Visible crew/equipment: When Nicky is dragging her ex-boyfriend across the hotel room floor you can see green screens outside of the balcony doors and windows. (00:39:45)
Continuity mistake: When Nick asks Dr. Ray what he's doing out on the Strip instead of at their crime scene, and Ray shows him the photograph of Madeline Briggs, his hand moves from the top of the photo to the bottom in consecutive shots. (00:03:20)
Continuity mistake: When Hodges shows Dr. Ray and Nick the information from Dede Chase's cell phone, Ray's arms change position between shots from the tabletop in front of him to crossed across his chest. (00:08:55)
Answer: He doesn't have the authority to arrest him - when anyone is arrested in the show, a police officer does it. Also he tells Ty that he is going to be submitting his case findings to Ty's insurance company, who would no doubt contact the IRS, who then would have him arrested for fraud etc.