As far as I know, data obtained using ECHELON or Predator or whatever they are are calling it this month, would not be admissible in court. The spying approach might work for the NSA, but the FBI needs data they can use in a court case.
Data that you can't use in court can still be very valuable. For example, if they can illegally determine whom to follow or where to look, then they can focus on collecting enough legally obtained information to paint a picture that gets them a warrant.
This would probably be considered fruit of the poisonous tree so would also be inadmissible. Whether the defence could show that to be the case though is another matter.
Correct me if I'm wrong, but the "No Fly List" doesn't come from a court, does it? That's why it's important that any kind of restriction or punishment be reviewed by and sentenced by a judge after due process. The ISP six-strikes policy comes to mind.