Okay, let me address the elephant in the room, even if it will make me even less popular than usual by doing so.
The big issue is with one paticular, sizable, culture for the most part. Namely that of "The Middle East". In general most of the rest of the enemies of the western world right now don't engage in terrorism. Even the global "bad boys" like Russia and China tend to act in a pretty straightforward fashion by leveraging with their military or economy rather than sending suicide bombers, or insurgent "commandos" to cause problems in other nations. Even when it comes to other poor nations with problems with say the US, Europe, etc.. culturally they tend not to engage in the same behavior.
This is not to say that only Muslims are terrorists, or capable of being terrorists, but simply that this is how things are the most common.
The problem with engaging in religious/cultural/ethnic profiling is of course that we have established moral principles where singling out a specific group is seen as wrong. Despite some rough spots for the most part we have made this work and view it as the correct course of action. I however feel current events over the last decade or so have shown that we were wrong, and that some of the fundemental assumptions inherant in that (ie that the dangerous stereotypes are false or present very little risk... a robbed house or two compared to the oppression of potentially millions of people being a small price) are wrong.
Right now I actually think we should re-consider our position on profiling in response to international events (as opposed to purely domestic ones). I in general have no real problem with "harassing" some Muslim (arabic, black muslim, or whatever though mostly the forum) when your dealing with the lives of hundreds or even thousands of people being lot from a single act. Not only do we have to worry about losing a plane to a bomb like decades ago, but as 9/11 has shown the plane's destruction itself can be a weapon. Even with just a bomb in flight if one was to say set it off during takeoff or landing at the right time a lot of damage could be done to the ground, not to matter timing things specifically for when the plane is flying over an urban area to douse it in debris and shrapnel or whatever.
In general I feel we should basically engage in profiling for mass transit (not just planes) at least as long as the current cultural conflict lasts. It needs to be carefully labeled legally though to prevent it from snowballing into purely domestic use. If this doesn't deal with the problem, then perhaps simply banning Muslims from using mass transit (subways, trains, planes, etc..) might be reasonable, as well as making it more difficult for people to come from The Middle East to the US in general which as "wrong" as it might sound doesn't strike me as being a bad thing when I read about failed terrorist attacks and such (of course stopping someone means far less to the public than a success).
I also think we need to get a lot more militant with our southern border. I've said this before, but I don't see the only issue with Mexico as being illegal immigrants and such. Allegedly a lot of insurgents and such (active terrorists, or just people "preparing", passing info, and other things, mostly the latter) get into the country via Mexio. In general an ethnic arab who acts the right way and picks up the language can "pass" as Mexican or South American at least for long enough. Then they can exploit the same pathways that illegals and such use to get into the US (tunnels under the border, illegal truck runs, etc...) and even find sympathy and assistance on both sides as odd as that might seem. Of course rather than helping Pedro find work to "feed his family" (despite the economic crisis), your helping some dude come in to hook up with "Abdul Bin Allah" (or pick your favorite terrorist sounding name). Oh sure, maybe all he does is print pamphlets or lurk around menacingly, but such people help form the infrastructure that ultimatly creates the suicide bombers and serious terrorists.
Simply my opinion. I do understand the whole arguement about how "if we do this we give into fear by compromising our standards", but let's be honest here... we're talking about stuff like nude body scans being directly at the entire populance. We're ALREADY sacrificing principles of privacy and so on. Frankly if we're going to bother to even consider something like that, we should instead look at specifically going after the group responsible and by the numbers we'll actually wind up infringing on less people (even if we wind up infringing on them to a greater extent).
