I think the basic issue is that since 9/11, "security" in all aspects of life, has definitely trumped "liberty" -- hence the famous Ben Franklin quote. The Bush Administration and the Congress in place in the 2001 timeframe both took the approach that "security" = "one nation under surveillance..."
The Constitution definitely took a back seat, if it was even in the conversation at all. "One nation under surveillance..." allowed all sorts of thing to happen unchecked. The no-fly and SSSS lists with no legal means of redress are just one example. People have mentioned Terry Stops versus ID checks. I think another example is that the TSA has really stretched the "in plain sight" standard. Since they have never identified the smallest item that could be a threat to an aircraft, everything is in plain sight, even in the smallest compartments of your carry-on or on your person.
The basic problem is that we who fly often are a relatively small minority of the population who has had our noses rubbed in the shredded Constitution. It's just not that big of a deal with the majority of Americans. As a matter of fact, I have seen enough evidence to make me believe that they think all this surveillance is a good thing, and, a lot of them resent the fact that we get to travel around the country and the world.
I think the real problem is not so much the Constitution as it is the implementing CFRs and the famous SOP. If there was a public comment period at all for a lot of these CFRs, virtually all comments were blown off or ignored. There were perfunctory legal reviews, mostly by Francine, the Googling TSA Lawyer, and like-minded individuals at Justice. I've seen some of the legal reviews (just look at some of the Privacy Impact Statements on line) and none of them pass the giggle test, even for this non-lawyer. The Kangaroo Court of fines is yet another example.
The good news is that the new DHS and TSA leadership can change the CFRs if pushed by the White House. Also, the AG staff can conduct a new legal review. I guess that's where I would start. There are lots of things that can be fixed without even filing a single lawsuit.