The Articles of Confederation were not perfect and had many problems. However, some of these were identified before the Constitution of the United States was written up.
The first major problem was that members of Congress were not showing up. To ratify anything, like a treaty or document, representatives from at least nine states needed to be present. Evidently, delegates back then didn't have respect for Congress meetings. For instance, Congress didn't have enough representatives for almost a month to sign the Peace of Paris. They even debated holding the meeting in a hospital where one of their number was ill!
Another of America's problems during this time was something which still haunts our country to this day: crippling debt. The costs of the Revolution were colossal, and Congress had to get money somehow to pay off their debts. However, they had none. The problem was that the states didn't agree to any of the money-raising strategies of Congress, which means that Congress was... STILL BROKE.
Too... Much... Freedom?
One of the greatest plagues of Congress was states not agreeing to their decisions. An instance of this was when Congress wanted to have some control over trade between the United States and different countries. They asked the states to let them for just fifteen years, but, guess what happened? The states didn't agree!