Deliberate mistake: Every time the investigators deal with IP-addresses, the addresses on display are impossible. Each of the four parts of an IP-address has to be between 0 and 255. As they do have to use IP-addresses some time, they could use addresses starting with 10. Those would be real addresses although not used as an official IP-address. This isn't the same as phone numbers using 555 - any IP address over 255 just wouldn't work. It would be like mentioning a phone number which uses the symbol for pi.
Deliberate mistake: When the runner is shot in the back of the head in the SUV, the bullet has come out the front of his head. However, blood is seen on the windshield instead of a bullet hole where the bullet would have continued to go through the glass.
Who Are You? - S1-E6
Deliberate mistake: A plumber is looking for a leak under the floor of a house, and sees the bones of a hand sticking out of the concrete wall at the side of the house. The concrete is flat, this is because in construction boards are put up and the concrete is poured in, so how were the fingers sticking out of the boards during construction? In reality, the fingers would be inside the concrete, the workman would see nothing, no plot for CSI.
Cats in the Cradle... - S2-E20
Deliberate mistake: A father, daughter (both construction\demolition experts) and the boyfriend try to frame the husband for attempted murder by planting a pipe bomb in her (wife\daughter\girlfriend's) car. The bomb is a stick of dynamite inside a pipe with 2 endcaps on it. A pipe is used to hold a improvised munition together: i.e., homemade explosives, or something like Anfo. The pipe provides the casing for the explosive material. Or, it is used to keep the shrapnel fragments around the explosives (like nails or pellets around a stick of dynamite). For dynamite, you simply drill a hole (in rock, in concrete, in whatever.) and drop the stick in. It needs no extra casing. The family would have known that. But the CSI crew needed some evidence to analyze and the blasting cap + detonator circuit would have given them nothing to study. The endcap with the hole drilled for the blasting cap was the case solver.
Cool Change - S1-E2
Deliberate mistake: Willows collects fingernail scrapings from Holly's left hand in the morgue for DNA matching to Holly's shooter. In the flashback, Holly uses her right hand to scratch her assailant while her left-hand remains gloved. (00:32:47 - 00:36:22)
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.