The chief objectionable feature of antitrust law is that there’s no “there” there. The Sherman Antitrust Act gives essentially no guidance to either businessmen or courts concerning what it bans; rather, it amounts to Congress’s handing the judges a blank check, letting them essentially make up their own rules.
While Earl Warren was chief justice of the Supreme Court, no defendant won an antitrust case before that court. While Ronald Reagan was president, prosecution of antitrust charges essentially stopped. People who decry as unconstitutional President Obama’s decision not to enforce the DOMA clearly don’t know very much history.
On the other hand, the Sherman Act is unconstitutional on two grounds: 1) it’s void under the 5th Amendment for vagueness; and 2) it’s a violation of the Delegation Doctrine, which — although much ignored by the courts nowadays — is the principle that Congress cannot hand off its legislative authority to the other branches.
Antitrust is economic nonsense too, as Bork, Easterbrook, and others have shown.