Almost nothing is forbidden. Security classifications apply only to those entrusted with legal access to classified information. Once the information leaks out[1], private citizens are free to publish it.
The exception is information related to nuclear weapons. That is Restricted Data, as opposed to classified, and is 'born secret.' It is forbidden to publish even if you independently discover it[2]. This has never been fully tested in the courts and many say it wouldn't stand up to judicial scrutiny, but I'm not so sure. The Constitution is not a suicide pact, and publishing information that can lead to the development of the most dangerous weapons known to man does not seem like the kind of thing that freedom of speech exists to protect.
[1] Certainly a crime for the leaker, but maybe also for the receiver if they provided material support for the act of leaking. I believe that is the theory for indicting Assange.
[2] You would of course have to know that you are not to publish such data. Presumably either because it is obvious (e.g. the plans for a nuclear bomb) or because you were told by a government official.
In the case of nuclear weapons specifically, it actually was a shock when the US tried to enforce the "born secret" doctrine (which said that information about weapon design and mechanics -- even if figured out from nothing but public, non-classified sources -- would automatically become classified as of the moment the person figured it out).
Amusingly, the argument was made -- and made seriously -- that the mere fact that the government had pursued the case was a leak of "born secret" information, since the attempt to suppress the information was tacitly an acknowledgment that it was correct (since incorrect information would not be subject to "born secret").
Sonoluminescence research was made substantially more difficult, because most of the modeling codes for collapsing plasmas were considered innapropriate to civiliian research... or so I have heard.
>Start taking pictures of policemen in your local area, especially near the station. I'm sure they will provide a guide to publishing...
You are allowed to photograph and film the police in public. Every US appeals court that has considered the issue has so ruled. It's possible that one of the circuits that has not considered the issue could rule the other way, but that seems unlikely.