I would say the most significant weaknesses of the government under the Articles of Confederation was the fact that the central government was too weak to enforce laws and couldn't impose taxes. The states had the most authority and since the government wasn't able to impose taxes, it doesn't have enough funds for a military (and it had to ask the states for troops). Without a strong military, it will be hard to defend the nation well if anything should occur.
The three branches of the government are the Executive, Legislative, and the Judicial branch. https://www.google.com/search?q=three+branches+of+government&rlz=1CAHPZQ_enUS786US786&source=lnms&tbm=isch&sa=X&ved=0ahUKEwi5v5jGr7HdAhVJTd8KHY9RCS8Q_AUICigB&biw=1536&bih=720#
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