What were the major arguments against the constitution put forth by the anti-federalists?

Perhaps the largest argument was that the Constitution did not grant enough power to the individual states. The Constitutional Convention was meant to REVISE the Articles of Confederation, not transfer power to the federal government. Another major complaint was that the Constitution did not initially contain the basic rights of normal citizens (the Bill of Rights). This was later added in order to convince the anti-federalists to ratify the Constitution.