In "Time and Memories" (Season 3), McGarrett became very emotionally involved when all evidence seemed to indicate that a former love of his life -- Cathy Wallis (Diana Muldaur) had murdered her husband. Danno told him he was losing his objectivity and needed to step down and let him, Kono, and Chin Ho complete the investigation. McGarrett declined to step down.
The fact of the matter is that McGarrett was a suspect, too! The episode did not mention that, but in real life, he would have been interviewed -- if not interrogated outright -- about his own whereabouts at the time in question. After all, he might easily have borne resentment toward Frank Wallis (unnamed) for taking Cathy from him and then mistreating her. Wouldn't that have seemed to an outsider to be a reason for Cathy calling him at 3:00 in the morning? If McGarrett had been investigated, how on earth would he have proven that he was at home, in bed, and asleep? It is much easier to prove that someone did something than did not do something.
To his credit, McGarrett did hang back after that and allow Danno to conduct the interviews and make the arrest. It may be one of the only episodes in which McGarrett did not confront the guilty party and tell him he was under arrest. How gratifying it would have been to watch McGarrett nab Arthur Dixon (Martin Sheen). Yet, from a legal point of view, the case was much stronger with Danno making the arrest.