Thank you FlyingRon and Some Random Guy for adding to my abbreviated post. Everything I wrote was accurate, by the way, FR - I just didn't have time to complete my post and my thoughts as other matters pressed (you should know by now that I
rarely limit myself to just 3 lines of text

).
I had planned to add that, despite broad First Amendment protections, the government has the authority in certain circumstances and under certain conditions to restrict both photo-taking and video-taking, and this holds true in airports with the photo-taking and video-taking of and at TSA checkpoints.
There was a Supreme Court decision in 1992 that ruled that public airport terminals are not "public forums," and "reasonable" regulations of and restrictions on First Amendment expressions are acceptable if the regulations and restrictions are not designed solely as an effort to suppress First Amendment rights (see
International Society for Krishna Consciousness, Inc v Lee, 505 US 672). Other areas that have been ruled by courts to be outside the public forum have been prisons, military bases, outside post office doors, and in federal courthouses (even sidewalks outside federal courthouses, until recently - see below).
Hence you have local ordinances, local laws and state statutes, as well as federal laws, that can regulate and restrict the taking of photos and videos in airports and elsewhere.
The First Amendment's protection of speech covers speech within public forums - public places historically associated with free expression such as public parks, public streets, public sidewalks - and the taking of photos and videotaping constitutes protected "speech" in these public fora. The Supreme Court has found that the sidewalk around the Supreme Court building, for instance, is a public forum, however inside the building there can be reasonable restrictions placed on First Amendment expression (see
United States v Kokinda, 497 US 720, 727-28, and
Greer v Spock, 424 US 828, 838, 1976).
It was just last month that a First Amendment/Civil Rights lawsuit filed by the New York Civil Liberties Union against the government, over the arrest of a photographer/videographer taking videos outside a federal courthouse, was settled, with the government conceding that photographing and videotaping on sidewalks outside federal courthouses was not prohibited by law, and prohibitions against such photo-taking and video-taking violated the First Amendment rights of free expression.
However,
Transit Authorities throughout the country often have
uncodified rules requiring the acquisition of a permit before photographing or videotaping within a transit system (see Massachusetts Bay Transit Authority, Florida's Miami-Dade Transit Authority, Washington Metro Area Transit Authority, New Jersey Transit, etc), many of these rules dating back to the early 1900s, and they have enforced these rules in the past (especially after 9/11), often by confiscating the film and photography equipment of permitless photographers and videographers, including that of the media.
And there are local ordinances and laws that can prevent photographing and videotaping if such expressions violate anti-loitering laws and disorderly conduct laws and/or if they interfere with public safety (ie. the flow of or obstruction of traffic). These "public safety" and/or security regulations are the type of regulations in place in many airports, and these are ones that
can allow for restrictions on photo-taking and videotaping at TSA checkpoints and often
are used to restrict photo-taking and videotaping.
SO, despite the TSA's policy that says it is fine and dandy to take photos and videos of and at checkpoints inside airports, arrests (as Some Random Guy illustrated with his link to the incident in San Diego) can be made, and have been made, when the photo-taking and video-taking is seen to be in violation of rules, regulations, local ordinances and laws, state laws, or federal laws.
That is why, in addition to TSA's stated policy that it is okay to take photos and videos at or of TSA checkpoints, the TSA has added the recommendation that travelers check with the specific airports they will be traveling to, through, and from to see what restrictions (local, state and/or federal) may be in place that could lead to an arrest for photographing and videotaping.
