Let's start with one that I find particularly grating.
DS9, "A Man Alone": They find no DNA, no evidence that someone else was in the holosuite at the same time as the murdered man, yet, none of them consider the possibility that he could have been killed... by a hologram!!!
DS9, "A Man Alone": They find no DNA, no evidence that someone else was in the holosuite at the same time as the murdered man, yet, none of them consider the possibility that he could have been killed... by a hologram!!!