Avigayil showed blood to David (and asked if it was Dam Nidah).
David: Do we inspect blood at night?!
Avigayil: Do we judge capital cases (e.g. to kill Naval) at night?!
David: He rebelled against the king (me), so he need not be judged.
Avigayil: Sha'ul is still alive, and you are not known to be the king.
David: "You spared me today from coming in Damim" - this connotes two bloods (Nidah and killing Naval).
Shabbos 56a (Rebbi): "Es Uriyah ha'Chiti Hikisa va'Cherev" - you should have judged Uriyah through the Sanhedrin, but you did not.
Kidushin 43a - Beraisa: If Reuven made Shimon a Shali'ach to kill someone (and Shimon did), Shimon is liable, but Reuven is exempt;
Shamai says, Reuven is liable - "You (David) killed him (Uriyah) with the sword of Amon".
The first Tana explains, just like you will not be punished for the sword of Amon, you will not be punished for Uriyah, because he rebelled against the king (he was Chayav Misah). Uriyah had said "Adoni Yo'av v'Avdei Adoni Chonim ..."
Sanhedrin 36a (Mishnah): In capital cases we begin with an intermediate Chacham.
Question: What is the source of this?
Answer #1 (Rav Acha bar Papa): "Lo Sa'aneh Al Riv" - we read this 'Al Rav'.
Answer #2 (R. Yochanan): "Va'Yachgeru Ish Es Charbo Gam David" (David was not the first to judge Naval to be Mored b'Malchus).
49a - The Sanhedrin (to Yo'av): Why did you kill Amasa?
Yo'av: He was Mored b'Malchus - "Va'Yelech Amasa...va'Yocher" (he delayed fulfilling David's request to gather Yehudah).
The Sanhedrin: This was not rebellious. Amasa expounded 'Ach' and 'Rak' to exclude. "Kol Asher Yamreh Es Picha...Rak Chazak ve'Ematz" excludes a command of the king contrary to Torah. When Amasa went to gather Yehudah, they were learning. Therefore he waited until they finished. Rather, you (Yo'av) were Mored (for supporting Adoniyahu's rebellion) - "Yo'av Nota Acharei Adoniyahu".
101b - Rav Nachman: Yarav'am lost (both) worlds on account of haughtiness - "Va'Yomer Yarav'am b'Libo..."
He knew the tradition that only Malchei Yehudah may sit in the Mikdash. He thought, 'When people see Rechav'am sitting and me standing, they will think that he is king and I am a slave. If I will sit, I will be Mored b'Malchus, they will kill me and serve him.'
Tosefta (Terumos 7:23): If Nochrim threatened a group 'give us someone and we will kill him. If not, we will kill all of you', they may not comply. If they specified someone, like (Yo'av requested) Sheva ben Bichri, they may comply.
R. Yehudah says, this is only if the Nochrim are in a position to kill all of them, for then it is better that everyone else not die. This was how the wise woman persuaded the city to hand over Sheva ben Bichri to Yo'av;
R. Shimon says, she told them that he was Mored b'Malchus, like anyone who rebels against Malchus Beis David.
Rambam (Hilchos Melachim 3:8): The king has permission to kill anyone who rebels against him.
Radvaz: This refers to a king appointed by a Navi, or someone that Yisrael agreed to appoint. We need not obey one who makes himself king by force.
Note: The Tosefta (Terumos 7:23) says that the woman who convinced the city to give Sheva ben Bichri to Yo'av told them that anyone who rebels against Malchus Beis David is Chayav Misah. Perhaps 'Beis David' stresses that he was a proper king, for he was appointed by a Navi.
Minchas Chinuch (407 DH v'Chol ha'Mored): Even though a king cannot pardon his honor, he is not obligated to kill one who rebels against him.
R. David (cited by Ran Sanhedrin 19b DH Mitzvah): A king cannot pardon his honor means that others may not disgrace him even after he pardoned his honor.
Igros Moshe (YD 2:60:3): One who is sentenced by Beis Din to die for an Aveirah is considered dead; anyone is allowed to kill him. This does not apply to someone liable for Mored b'Malchus, for the king can pardon him. Also a Nochri king may kill one who rebels against him, and it is not considered murder. Nevertheless, since he is not liable according to Torah law, it is a Mitzvah for others to save him if they will not be considered Mored b'Malchus for doing so. The Mitzvah of "U'Vi'arta ha'Ra mi'Kirbecha" does not apply to one who was Mored b'Malchus; one is not obligated to testify. However, surely the king wants people to do so; it is as if he explicitly commanded. Sha'ul killed the Kohanim of Nov for not telling him about David. Had David truly been Mored b'Malchus and had they known, he would have been justified in killing them. The Hagahah in Noda bi'Yehudah (2:YD 74) DH Emnam says that according to the opinion that Mored b'Malchus must be judged, Sheva ben Bichri was not considered Mored b'Malchus. However, people were obligated to hand him over to Yo'av for judgment; they had no reason to suspect that Yo'av would do improperly. The Hagahah connotes that after judgment he is considered dead, like others judged for Chayavei Misas Beis Din. This is wrong.
Rambam (ibid.): Even if he commanded someone to go to a certain place or not leave his house and the person disobeyed, he is Chayav Misah - "Kol Ish Asher Yamreh Es Picha...(Yamus)."
Tosfos ha'Rosh (Kidushin 43a DH Mored) and Tosfos (Shabbos 56a DH d'Omar): Rashi says that Uriyah was Mored for calling Yo'av 'Adoni' in front of David. This is not Meridah, to honor the king's servant in front of the king. He did not intend to make Yo'av king! Rather, he was Mored for not going home like David commanded. Some say that his Meridah was mentioning Yo'av before David.
Tosfos (Yoma 66b DH Mahu): Calling Yo'av 'Adoni' in front of David is Meridah according to the opinion that one may not honor a Talmid in front of his Rebbi.
Rambam (ibid.): Similarly, he may kill anyone who disgraces the king or curses him, like Shim'i ben Gera. He may kill only through the sword. He can imprison and lash people for his honor. He cannot make people's money Hefker. If he does so, this is theft.
Source (Zalman Wilner, cited in R. Akiva Eiger, Gilyon ha'Rambam): When Shim'i cursed David, David promised that he would not kill him by the sword. This is meaningful only if a king may not kill in other ways. This is why the Rambam teaches this after the Heter to kill someone like Shim'i.
Rambam (9): If Reuven was engaged in a Mitzvah, even a light Mitzvah, and therefore he was Mevatel the king's decree, he is exempt. The Master's words come before the slave's. All the more so, if the king commanded to Mevatel a Mitzvah we do not heed him.
Question (Tosfos Sanhedrin 36a DH Rabah): The Gemara says here and in Shabbos (56a) that Sanhedrin must rule that one is Mored b'Malchus. In Megilah (14a) it says that he need not be judged!
Answer #1 (Tosfos): Sanhedrin must hear testimony and verify that he is Mored. He need not be judged like other capital cases, e.g. that we cannot Mechayev him until the next day. Rather, we can Mechayev him immediately.
Question (Turei Even Megilah 14b DH Mored): David was criticized for not judging Uriyah through Sanhedrin. If he was not judged k'Halachah, there was not a proper Gemar Din, so he is fully liable for his death (Makos 5a)!
Answer #2 (Turei Even): Mored b'Malchus need not be judged. However, if there is any question about the kingship or the rebellion, Sanhedrin must clarify the matter. However, this is a mere Giluy Milsa that he was Mored b'Malchus even before the verdict. Regarding Naval, the question was whether David was anointed to be king immediately, or only after Sha'ul will die. This is why David was able to be on the Sanhedrin, even though a king cannot be. If David was truly king, Naval is already Chayav Misah!
Answer #3 (Noda bi'Yehudah 2:YD:74 DH ume'Atah): A Tosefta says that we may give over a Yisrael for Nochrim to kill only if it is like Sheva ben Bichri. Reish Lakish (Terumos 47a) explains that he was Chayav Misah. He holds like R. Shimon in the Tosefta, who says that Sheva ben Bichri was Mored b'Malchus, i.e. even though he was not judged. The Gemara in Megilah is like him. R. Yochanan (ibid.) explains that it must be like Sheva ben Bichri, i.e. if we do not hand him over all the Yisraelim will die. He holds like R. Yehudah in the Tosefta. The Gemaros in Sanhedrin and Shabbos are like him.
Answer #4 (Merumei Sadeh Megilah 14a DH v'Chidush): Avigayil rebuked David only for judging at night, not for the judgment itself. She held that David was not known to be the king, so Naval was not Mored b'Malchus. We must say that Naval was like a Rodef. He called David 'a slave who rebelled against his master'; perhaps he would tell Sha'ul. David was not so careful to judge him k'Halachah for Rodef because he could always declare him to be Mored b'Malchus. Anyone whom the king considers to be Mored is called Mored b'Malchus, even without Sanhedrin. It would have been Midas Chasidus to judge Uriyah through Sanhedrin; David was criticized for not doing so. It seems that this is the Rambam's opinion.
Note: The Merumei Sadeh implies that a Rodef must be judged during the day. This is difficult. One may kill a Ba b'Machteres at night!
Chasam Sofer (OC 208 DH v'Ya'an): A king cannot punish at will. We learn that Mored b'Malchus is Chayav Misah from "Kol Ish Asher Yamreh Es Picha". It is not clear how a Navi (Yehoshua) was able to Mechadesh this. The Ramban (Mishpat ha'Cherem) learns from "Kol Cherem... Mos Yumas" that a king or all of Yisrael can forbid something using Cherem, and one who transgresses is Chayav Misah.
Chasam Sofer (EH 1:151 DH v'Lu): Kam Lei bid'Rabah Minei does not apply to one who is Chayav Misah to the king. It is lighter than other Chiyuvei Misah. Mored b'Malchus is only b'Mezid, but it does not need Hasra'ah.
Shach (CM 348:6): The Maharshal says that Yo'av was Mezid for causing Uriyah to die. The Gemara connotes otherwise. Yo'av had to suspect that Uriyah was Mored b'Malchus, and that David had a reason not to kill him through the Sanhedrin. Both of these were true; David did not want people to think that he killed him in order to take his wife.