But it raises a question how Starfleet can allow such a person in the chair. It reflects badly on them.
I would imagine they would do intensive psych evals not only when applying to the academy but also when they are being considered for captaincy. He would likely have passed that. Despite what Gene wanted you to think as TNG began, humanity has and will always have baggage.
Okay so I must have missed something. In one of the episodes of this season Worf states that he's the slayer of Gowron. When did this happen? I don't remember this happening on TNG. Was it on DS9 or something?
Last handful of episodes of DS9, yes.