What was the major weakness of the Articles of Confederation?

Generally (though it's a bit of a circular answer to say so) the biggest weakness of the government under the Articles of Confederation was that it was too weak. The Articles simply didn't grant the national government enough power to govern the thirteen states as a nation. More specifically, I would argue that under the circumstances the most glaring weakness was that the government under the Articles lacked the power to levy taxes. The United States emerged from the Revolution as an independent nation, but one with a  great deal of war debt. This threatened the credit of the nation abroad, making it difficult to secure new loans. Congress under the Articles could request funding, but could not force the states to contribute tax revenue. This made it almost impossible to fund the federal debt. So perhaps the most urgent shortcoming of the government under the Articles had to do with its inability to raise revenue. This issue was just one of several that led to calls for a new constitution in 1787.