An effect of the new territory acquired by the us after the mexican-american war was that states disagreed about

 States disagreed about whether slavery should be allowed in the new territories.

Explanation:

The Mexican Cession was the large region of land that Mexico ceded to the United States in the Treaty of Guadalupe Hidalgo in 1848.  It included territory that would later become the states of California, Nevada, Utah, and parts of what would become Arizona, New Mexico, Colorado and Wyoming.  The Mexican Cession reignited tension on the issue of slave-holding states vs. free states.

The Missouri Compromise (1820) had admitted Missouri into the Union as a slave state with Maine being added at the same time to keep the balance of slave and free states equal.  It also prohibited any future slave states north of the latitude line 36 1/2 degrees north of the equator in territories of the Louisiana Purchase, with the exception of Missouri (north of that line) being admitted as a slave state.  Since that latitude line ran right through the middle of the Mexican Cession territory, there was bound to be further debate over the issue of slave vs. free states.