Apropos Orin's post, two thoughts:

(1) The argument that the police can't aim radiation surveillance devices at homes (and likely businesses, mosques, and the like) without a warrant is a nontrivial one: It's basically Kyllo v. United States (no aiming heat sensors at homes without a warrant) meets Mincey v. Arizona (no special Fourth Amendment exceptions for investigations of very serious crimes). I discuss this in this Slate piece from 2002.

My ultimate conclusion is that such radiation surveillance from outside the buildings should be constitutional, because what's an "unreasonable search" when looking for drugs (or even for evidence of murder) becomes reasonable when looking for radiation weapons: "[F]inding dirty bombs must simply be different from fighting normal crime. Searches for weapons of mass destruction can't be treated like searches for marijuana-growing devices or even for murder weapons." Others have argued that it might be constitutional for another reason -- searches that are likely to reveal only evidence of contraband (which, the argument would go, includes searches for radioactive materials but not for heat sources) don't invade any reasonable expectation of privacy; I'm not as wild about that theory, but I agree with its bottom line. Nonetheless, I think the Slate piece may help explain the nature of the argument that such searches are unconstitutional.

(2) Orin points out that "In numerous cases, the monitoring required investigators to go on to the property under surveillance, although no search warrants or court orders were ever obtained, according to those with knowledge of the program." I want to caution people against assuming that going onto the property under surveillance without a warrant is per se unconstitutional under existing law. There are various reasons why entering the property wouldn't itself be treated as an unconstitutional search, for instance if the parts of the property that they entered was generally open to the public, or if the property was the urban equivalent of "open fields" as opposed to the inside of someone's building (or the "curtilage" of that building).

Some of these doctrines are quite complex and unsettled, and I don't want to go into them in detail here; and I also want to stress that even if entering the property wasn't a search, doing some things on that property (perhaps including measuring radiation, or perhaps not, see item 1 above) may well be a search. But people should realize that whether "go[ing] on to the property under surveillance" is unconstitutional without a warrant is a difficult question.