Except in Illinois and Massachusetts, it's only eavesdropping if there is an expectation of privacy. The other 10 states have spelled that out in the statute.
Unfortunately, this isn't stopping the cops from laying charges.
Mister Cat it certainly has been held Constitutional in some of those states and since it has never successfully gone up through a Federal appeal based on the U.S. Constituion, we don't truly know the answer.
Here's a story about a Maryland case. Anthony Graber was charged for posting a Utube video of a trooper in street clothes pulling him over and rousting him at gunpoint.
The judge threw the case out, saying that a cop on duty in a public place has no expectation of privacy, so it wasn't eavesdropping.