What were three major limitations of the Articles of Confederation, and how did they impact the new nation?

Almost all of the major limitations of Articles of Confederation were due to the lack of a strong Federal government. Three of the major areas that this arrangement significantly limited were defense, trade, and taxation. The years between 1781 and 1787 were most certainly a period of chaos and conflict.
With the power to levy troops centered in the various states, raising and maintaining a standing army was a tenuous affair until the ratification of the Constitution. This military weakness allowed the British and Spanish to behave aggressively at the borders of the nascent United States. A paramount example of this aggression was the British occupation of the Northwest Territory, something disallowed by the Treaty of 1783.
Trade famously suffered between individual states and with foreign governments. Under the Articles, individual states printed their own coinage and determined their own monetary and trade policies, which made business between the states extraordinarily difficult. Foreign powers were hesitant to sign trade agreements with the United States, as there was no guarantee that all the states would ratify them.
Underlying many of the problems of the young United States was the inability to reliably collect taxes for any large expenditures. The inability to consistently fund the army was perhaps the most hobbling difficulty. The inability of Congress to pay the soldiers after the war led to the states paying the returning soldiers in currency that was often virtually worthless.
The Articles of Confederation produced a chaotic and disjointed collection of states, described by George Washington as joined together by "a rope of sand."