Final answer:
Stephen Douglas's mistake was underestimating northern opposition to the expansion of slavery through the Kansas-Nebraska Act, which allowed the decision of slavery to be made by settlers via popular sovereignty.
Step-by-step explanation:
One of Stephen Douglas's mistakes in proposing the Kansas-Nebraska Act was underestimating the depth of northern opposition to the spread of slavery. When Douglas proposed the act, he likely did not anticipate the strong reactions and eventual violent confrontations it would provoke, especially in regards to the issue of slavery in new territories. The act allowed for the possibility of slavery in Kansas and Nebraska through the principle of popular sovereignty, which overturned the Missouri Compromise line and enraged many in the North who opposed the expansion of slavery.