What issues did the Compromise of 1850 leave unsettled?
The Compromise also didn't specify a practical, straightforward method by which states would hold the elections that decided the issue of slavery for their territory. So it was left to Congress to pass individual laws like the Kansas-Nebraska Act. The idea of popular sovereignty sounds great - very democratic - but in practice it was a disaster and led to Bleeding Kansas. So the Compromise left the elections issue unresolved, and provided no national military security so they could be carried out.
While re-emphasizing the Fugitive Slave Act, it provided no practical means for its enforcement, and this would be a thorn in southern slaveholders' sides in the years leading up to the war, as they had the mistaken impression that the North was full of abolitionists when in fact, it was not.
At best the Compromise was a stalling measure, intended to postpone the issue of slavery until a later date. The Civil War represents the failure of that future compromise.
In the end, the Compromise of 1850 left the issue of slavery unsettled. The Compromise was a reflection of the time period's false belief that the issue of slavery could be something that was negotiated away. In resting the issue of slavery into the hands of geographic border division and thinking that keeping the balance of slave and free states equal is essential, the framers of the Compromise such as Henry Clay ultimately refused to take an stand on slavery. In the end, initiatives such as the Compromise of 1850 helped to actually worsen the North and South antagonisms, and might have done more harm than good in starting the Civil War in that it could not resolve the issue of slavery in a finalized way.
The main issue that the Compromise of 1850 left unresolved was the issue of where there would and would not be slavery.
The compromise did not specify whether slavery would be allowed in various territoires -- it left that up to the "popular sovereignty" of the territories involved.
More generally, the compromise did not solve the main issue of slavery itself. It did not solve the problem that was created by having two regions of the country with different systems, each side distrusting the other. It left both sides still angry with the other and dissatisfied with the compromise.
The passage of the Compromise of 1850 was a great achievement of practical politics, but it left many things unsettled but a few things famous and settled. It staved off civil war for another decade. The movement for southern secession quietly receded for the time being. Southerners interested in expanding the domain of slavery increasingly turned to the idea of annexing Cuba.
It allowed the immediate admission of California as a free state. As a result of the gold rush, California’s population soared. Statehood allowed the federal government to stabilize law and order in California. By endorsing popular sovereignty, the compromise asserted the right of Congress to legislate for the territories on the slavery issue. One of Calhoun’s contentions was that because the territories were common property, Congress had no authority to legislate against the ownership of the property of some citizens. On the other hand, the great weakness of popular sovereignty was its assumption that settlers in the territories would be willing to arrive at peaceful conclusions to the slavery question.
The compromise also created a new Fugitive Slave law to succeed the original Fugitive Slave Law of 1793. Originally, this was the most unnoticed part of the compromise. However, it was a time bomb waiting to explode, because its terms threatened to make every northerner complicit in slave pursuit and rendition. The compromise made Douglas a nationally famous figure. Douglas was reelected to the Senate in 1852. He now began to be spoken of as a possible presidential candidate.