What is useful information ? This is likely to be debated quite a bit in the USA with increasing intensity after January 20 2009. The Bush administration has justified many of their crimes by claiming that they provided "useful information" about al Qaeda. This would not be a justification if it were true, but is it ?
One way to decide is to look at all of the data collected via torture, warrantless wiretapping, "enhanced interrogation," and torture outsourced through rendition and see if there is useful information in there. This is setting the bar too low, not just morally but also to decide what is and what is not useful information.
There is no law of conservation of useful information. If a mixture of useful information and falsehoods contained the same amount of useful information no matter how numerous the falsehoods, then we could get useful information out of chimpanzees hitting random keys.
This is obvious of course (hey you're reading it here). If the statement "P" is useful information so is the statement "'P' is true" however the two statements
"'P' is true" and "'P' is false" together amount to "'P' is meaningful" which we can determine just by thinking about "P".
No doubt given information on al Qaeda obtained via reliable methods, it will be possible to search the pile of data generated by the Bush administrations criminal means and finde similar statements. In this case the useful information was provided by the search (one of whose ingredients was the useful information).
Only if the cost of the miss-information and diss information in which the valid information is buried is considered can we decide if the mass of data was useful or not.
I'd guess that the fact that we learned via torture outsourced to the Egyptians of Ibn al Shaik al-Libi the falsehood that Iraq was teaching al Qaeda terrorists to use chemical and biological weapons by itself will outbalance all useful information actually obtained via illegal means.