The actual US Code of Section 605:
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TITLE 47 > CHAPTER 5 > SUBCHAPTER VI > § 605
§ 605. Unauthorized publication or use of communications
(a) Practices prohibited
Except as authorized by chapter 119, title 18, no person receiving, assisting in receiving, transmitting, or assisting in transmitting, any interstate or foreign communication by wire or radio shall divulge or publish the existence, contents, substance, purport, effect, or meaning thereof, except through authorized channels of transmission or reception,
(1) to any person other than the addressee, his agent, or attorney,
(2) to a person employed or authorized to forward such communication to its destination,
(3) to proper accounting or distributing officers of the various communicating centers over which the communication may be passed,
(4) to the master of a ship under whom he is serving,
(5) in response to a subpena issued by a court of competent jurisdiction, or
(6) on demand of other lawful authority. No person not being authorized by the sender shall intercept any radio communication and divulge or publish the existence, contents, substance, purport, effect, or meaning of such intercepted communication to any person. No person not being entitled thereto shall receive or assist in receiving any interstate or foreign communication by radio and use such communication (or any information therein contained) for his own benefit or for the benefit of another not entitled thereto. No person having received any intercepted radio communication or having become acquainted with the contents, substance, purport, effect, or meaning of such communication (or any part thereof) knowing that such communication was intercepted, shall divulge or publish the existence, contents, substance, purport, effect, or meaning of such communication (or any part thereof) or use such communication (or any information therein contained) for his own benefit or for the benefit of another not entitled thereto. This section shall not apply to the receiving, divulging, publishing, or utilizing the contents of any radio communication which is transmitted by any station for the use of the general public, which relates to ships, aircraft, vehicles, or persons in distress, or which is transmitted by an amateur radio station operator or by a citizens band radio operator.
(b) Exceptions
The provisions of subsection (a) of this section shall not apply to the interception or receipt by any individual, or the assisting (including the manufacture or sale) of such interception or receipt, of any satellite cable programming for private viewing if—
(1) the programming involved is not encrypted; and
(2)
(A) a marketing system is not established under which—
(i) an agent or agents have been lawfully designated for the purpose of authorizing private viewing by individuals, and
(ii) such authorization is available to the individual involved from the appropriate agent or agents; or
(B) a marketing system described in subparagraph (A) is established and the individuals receiving such programming has obtained authorization for private viewing under that system.
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Before you jump on the exception for 'ships, planes, and persons in distress', be aware that routine police/fire comms do NOT fall in this category. This means SOS/MAYDAY level immediate life and death emergency situations only. It's intended to let you notify authorities of calls for help you happen to receive, legally.
The ECPA states specifically that you may monitor police/fire stuff personally. It does NOT, repeat, NOT, remove the prohibition against divulging/publishing/revealing the existance of a communication.
All of this is 'unsettled' law. There are apparently decisions in all directions. That means that if your local law has a prosecutor willing to prosecute under this law, you get to spend your life savings (and more) in court fighting it. Few would consider running a scanner stream worth bankrupting themselves.