Gizmodo reports that the iPhone 4 lawsuits have started:

The first iPhone 4 class action suit against Apple and AT&T has been filed today in the United States District Court for the District of Maryland. The lawsuit focus on the antenna design problems, making several claims...
This suit is claiming:
  • General Negligence (APPLE and AT&T)
  • Defect in Design, Manufacture, and Assembly (APPLE)
  • Breach of Express Warranty (APPLE)
  • Breach of Implied Warranty for Merchantability (APPLE and AT&T)
  • Breach of Implied Warranty of Fitness for a Particular Purpose (APPLE and AT&T)
  • Deceptive Trade Practices (APPLE and AT&T)
  • Intentional Misrepresentation (APPLE and AT&T)
  • Negligent Misrepresentation (APPLE and AT&T)
  • Fraud by Concealment (APPLE and AT&T)

Besides the antenna issues listed in this lawsuit, others are complaining the new glass design breaks if it falls out of your pocket or you drop it, and many complain the phone randomly says there's no sim card making people reboot over and over to get rid of that error among other things.