Fight Night - S3-E7
Plot hole: A large part of Nick's plotline revolves around the discovery that the couple's stolen ring has a fake diamond switched out for the real one. But the ring was left as collateral for a very expensive necklace for the woman to wear that night. There is no way that a jewelery store would accept a ring for collateral without appraising the ring's/stone's value first. And in that inspection, they would have discovered the switch and not accepted it.
Random Acts of Violence - S3-E13
Plot hole: While searching through the dead computer guy's CDs Nick finds a CD supposedly burned that night, containing data gathered at the time of death, but by the time the CD was burned the guy would have already been dead, so who took it out of the computer and filed it away?
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.