Stalkerazzi - S2-E15
Plot hole: The photographer who found the dead guy (Stalkerazzi) told Horatio that he was chasing a black Cadillac Escalade that was chasing the Stalkerazzi's car. He also said that he got stuck behind a truck and that when he finally caught up the Stalkerazzi was dead and there was no sign of the black Escalade. Throughout the rest of the episode nobody does any looking into the black Escalade, asks suspects if they own one or even mention it again. No investigation of the truck that the photographer got stuck behind was shown either. In the same episode Speed tells a cop, while in a tree looking into someone's yard, that they go in through windows if need be to close a case. This is totally inconsistent with the rest of the show and the law. They are always careful about getting search warrants and doing things By the Book.
Death Grip - S2-E4
Plot hole: There is absolutely nothing that would give Horatio any reason to think the severed arm they found was from a previous victim of their suspect. It doesn't make any sense he would pick something as random as the arm that has no connection (other than it being found during the search for the girl) to the case.
Plot hole: Alex determines the actress is only about 18 because her wisdom teeth haven't erupted yet. The problem is they don't always erupt, I'm 32 yrs old and mine have never erupted.