The Alternative Amedment Process

The Congress... on the Application of the Legislatures of two thirds of the several States, shall call a Convention for proposing Amendments, which... shall be valid to all Intents and Purposes, as part of this Constitution, when ratified by the Legislatures of three fourths of the several States....

--The Constitution of the United States, Article V

One of the unused portions of the Constitution is the clause allowing states by convention to pass constitutional amendments. I was wondering what people thought about this option, and whether it could be used to fix some of the more glaring problems (whatever you think they may be). Do people think that it would be an effective alternative, and if so, what would you use it for?