Plot hole: The FBI is looking for a "very tall" guy who has been identified as such by various witnesses and by their own expert due to the entry angle of a fatal bullet wound - 6'5" at least. They send Elena into a bar near the end of the show to meet the Albanian perp who when he arrives is barely average height.
The Cat Who Cried Wolf - S1-E7
Plot hole: Magnum finds the cat with the bloodied paws. He takes the cat home, arranges with Higgins what to do, brings it back where he found it, and tails it for "over an hour", Higgins says. Finally finds where it came from, and in the house there's a corpse. Shenanigans ensue, Magnum comes back with the police to a now empty house and he tells to Katsumoto that it was not empty "a couple hours ago" and is amazed at how quickly and efficiently the bad guys must have cleaned. The problem is; later we see through the security cameras what happened, and how Max the cat got the blood on its paws. Supposedly the villain did an ultra-efficient job cleaning everything up after Magnum's visit...but what about before? Magnum arrived a good 2 hours after the homicide. What on Earth did the killer do during that time? The dead guy was still lying around in a pool of blood, and the bad guy hadn't even picked up his own ski mask! Forget it. He did not even close the front door.