What problems did the new territory west of the Appalachian Mountains pose and how effectively did Congress handle those problems in the 1780s?

In addition to the valid points made in the post above, there were other considerations and issues concerning that territory at the time as well.

1)  It was populated mostly with Native Americans, a handful of American trappers, a few French missionaries and fur traders and nothing else.  It was wild and largely uncharted, therefore, it was difficult to control.  What's more, through two wars, the French and Indian War and the Revolutionary War, Native tribes had been armed and encouraged into the fight.  So now the Natives remaining were suspicious, carried a grudge and had something to shoot with.  There was no Congressional solution to this except to encourage westward migration - essentially having settlers fight their battles for them.

2)  The country was governed by the Articles of Confederation, which emphasized power to the states.  There would be competition for the land to the west, and varying ideas on how to settle and organize it.  Congress dealt with this problem fairly effectively under the Land Ordinance of 1785 which split the country into new states and provided for their organization and admission into to the Union once a population threshold was reached.  It is one of the few accomplishments of government under the A of C.