What were the most divisive issues the Constitutional Convention faced and what compromises did the delegates reach to solve them?

The Constitutional Convention certainly faced its share of controversies in its attempt to redesign the government of the United States. In fact, even the project of creating a this new, more centralized government for the United States was quite controversial at the time (this controversy can be observed in the Federalist Debates which surrounded the Constitution's ratification, where proponents and critics of the Constitution argued for and against the new founding document). However, there were several issues that arose over the course of the Convention itself which divided the members of the Convention against each other, and had to be navigated via careful compromise.
One of the most heated disagreements arose between the less populous states of the Union and the more populous ones over the question of how much representation each state should receive in the legislature. The more populated states put forward the Virginia Plan, which suggested that representation be proportionate to population (naturally, this idea would favor these larger states politically, as they would elect more delegates to Congress). In contrast, the New Jersey Plan, backed by the smaller states, envisioned a legislature in which each state received an equal vote. Neither side was willing to concede. The Great Compromise offered a solution: by dividing Congress into two houses, it would be possible to preserve an element of each plan. The House of Representatives would be organized along the lines of the Virginia Plan, and the Senate more along New Jersey Plan lines, with each state receiving the same two Senators. Thus, both sides in the debate could be appeased.
A second point of division was over the question of slavery. One of the critical questions that emerged during the Constitutional Convention was whether slave populations should be counted when determining each state's representation in Congress. Slave States argued for their inclusion (as slaves made up a significant portion of their population) while Free States opposed this measure vociferously. In the end, the members of the Convention adopted the 3/5 Compromise, which held that slaves would count at 3/5 the value of a free citizen. Another point of contention concerned the Slave Trade itself. This second question was tabled until 1808, at which point Congress could legislate its prohibition.