The biggest problem with the Articles of Confederation was that it gave too much powers to the individual states and did not enumerate enough powers to the federal government. The abuses of King George III and the British were very fresh on the minds of Americans, and they were reluctant to give too much power to the national government out of fear that it might infringe upon their rights in the similar fashion.
Along those lines, the second problem was that the national government did not have the power to tax, which left the nation dependent upon the states sending revenue to the federal government. America was quickly lost financial stability under this plan, and the sale of land was the chief reason their were able to make ends meet.
The final problem was the ability of the Articles to make laws but the inability of the national government to enforce them. Again, that power was given to the states. This impossible situation was exposed by Shays's Rebellion. The states were unable to quell the resistance, but the national government didn't have the authority to intervene resulting in an unacceptable period of lawlessness. This situation was perhaps the greatest catalyst in causing Americans to look at their situation and realize that a change was needed to their government if America was going to be able to prosper in the future.