I don't think anything should necessarily be changed. Perhaps declaring the US to be a Christian country. Banning gay marriage. Making English the official language. Make flag burning a crime.A new Constitutional Convention would be the worst thing that could possibly happen to this country.
But in the end...a Constitutional Convention would cause more uproar than anything. Could you imagine a media blackout while Nancy Pelosi and her ilk try to take away guns and free speech? Or Ted Cruz trying to turn the US into canada?
Congress doesn't sit on an Article 5 convention, they just have an obligation to call it and pay for it. Of course they have received collectively more than 600 requests from all 50 states for a convention and have ignored their responsibility so far.