The Single Biggest Weakness of the Constitution:
Lots.
The ambiguous wording of the 2nd Amendment ranks high up there.
Having a directly elected President is another.
Giving that President a hand in lawmaking (veto), violating the separation of powers, would qualify.
Giving the Senate a say on matters not materially affecting how the Several States are being run was truly a horrendous, unforced error, as was making treaties subject of Senate ratification (another violation of the separation of powers), as was giving all States, no matter their population, two votes.
Letting the Several States run Federal elections was just gross. Setting up a FPTP, winner-takes-all voting system was worse, still.
The biggest of all is the missing text in the 1st Amendment, that should have read like, "Under no circumstances whatsoever, and in no context, and no matter how it is used or intended to be used, does money, or any other thing of value, changing hands equal Constitutionally protected speech."