Erebor laws
The general laws of Sigin-Taragathol are not many, but all are expected to know and abide by them. The first law of Erebor's Halls is that none may carry weapons, for the Halls are under the protection of Dain Ironfoot and the Baruk Narag (the Black Axes, who are Dain's personal bodyguard and Erebor's "police" force). Disobeying this law will usually result in the confiscation of said weapon and the payment of a relatively small fee. Repeated breaking of the law may carry some time in jail. Of course, Dwarves with legitimate reasons to bear arms within Erebor are excused from this law.
Most problems that arise would usually be handled by each clan, depending on the importance of the fault. Any problem that affects only the clan will be dealt with by the clan, usually by the clan elders and the Thane. If a problem involves several clans, it will be taken to the Court. There, one Elder from each clan will sit to hear the case, and then a decision will be taken based on a majority-vote basis. In very special cases (usually those involving the security of Sigin-Taragathol itself, or in very special circumstances like attacking a guest, or killing or severely wounding another dwarf), the Grand Court may called. This court involves the four Thanes of the clans (or a representative of the Thane), and King Dain himself. Punishments issued by the Grand Court are harsh most of the time, for the crimes involved are considered the most serious.
A final note: On fistfights.
Fistfights are not unheard of events in Erebor. Fistfights are troublesome, but hardly anything major; the Dwarves, being an ingenious and practical folk, have a special law for them. Those involved in the fistfight will pay for any damages done during its course, no matter who started it. Moreover, such a disturbance of the peace will result in imprisonment of one to 5 days, plus the payment of a fee. All are warned!