"We don't prohibit public, passengers or press from photographing, videotaping, or filming at screening locations. You can take pictures at our checkpoints as long as you're not interfering with the screening process or slowing things down. We also ask that you do not film or take pictures of our monitors."
--the article does go on to note that state laws or local ordinances may prohibit filming.
And then she posts advice from Ms. Smith's "Privacy and Security Fanatic," which is that
"if you do videotape TSA checkpoints, then you should have the TSA public affairs (TSA's Office of Strategic Communications) number plugged into your phone: (571) 227-2829. Another important phone number to have with you is the TSA's Office of Civil Rights at (571) 227-1917."
Ms. Smith goes on to tell some stories of people who have been challenged at airport screening stations for shooting video. Important note, it's probably wise not to take off your pants except your underwear while doing this.
So, go ahead, and video, but know your rights and "stay calm and polite at all times." You could be the next You-tube sensation.