How we cite our quotes: (Act.Section.Line)
Quote #1
[…] with said boundary line to the place of beginning be, and the same is hereby, erected into a temporary government, by the name of the Territory of New Mexico: Provided, That nothing in this act contained shall be construed to inhibit the government of the United States from dividing said Territory into two or more Territories […] And provided, further, That, when admitted as a State, the said Territory, or any portion of the same, shall be received into the Union, with or without slavery, as their constitution may prescribe at the time of their admission. (Texas.Section 2.2-4)
You could consider this as threat to Texas, given that Texas was considering invading New Mexico to get its land back. We can chop you up even smaller, the guv'mint is telling them.
Quote #2
And be it further enacted, That the executive power and authority in and over said Territory of New Mexico shall be vested in, a governor, who shall hold his office for four years, and until his successor shall be appointed and qualified, unless sooner removed by the President […] he may grant pardons for offences against the laws of said Territory, and reprieves for offences against the laws of the United States, until the decision of the President can be made known thereon. He shall commission all officers who shall be appointed to office under the laws of the said Territory, and shall take care that the laws be faithfully executed. (Texas.Section 3.1, 3
The Compromise statutes make sure there's someone in charge in the territories to get things up and running. Governors, Commissioners, officers—the territories are practicing being states.
Quote #3
And be it further enacted, That there shall be a secretary of said Territory, who shall reside therein […]he shall record and preserve all the laws and proceedings of the legislative assembly hereinafter constituted and all the acts and proceedings of the governor in his executive department ; he shall transmit one copy of the laws and one copy of the executive proceedings, on or before the first day of December in each year, to the President of the United States, and, at the same time, two copies of the laws to the Speaker of the House of Representatives and the President of the Senate, for the use of Congress. (Texas.Section 4.1)
Even in 1850, rules meant tons of paperwork.
Quote #4
And be it further enacted, That it shall be the duty of all marshals and deputy marshals to obey and execute all warrants and precepts issued under the provisions of this act, when to them directed ; and should any marshal or deputy marshal refuse to receive such warrant […] or to use all proper means diligently to execute the same, he shall, on conviction thereof, be fined in the sum of one thousand dollars […] and after arrest of such fugitive, by such marshal or his deputy, or whilst at any time in his custody under the provisions of this act, should such fugitive escape, […] such marshal shall be liable, on his official bond, to be prosecuted for the benefit of such claimant, for the full value of the service or labor of said fugitive in the State, Territory, or District whence he escaped. (Fugitive Slave Act.Section 5.1)
The Fugitive Slave Act section of the Compromise is an attempt to maintain order by appeasing the South. Here, order is kind of aggressively maintained by setting rules that punish officials who don't uphold the law. Underneath all that complicated language is a simple: track down the runaway slaves or pay up big time.