What do you suggest? Let the muslims do what they will and arrest them after they have murdered thousands more? I see your point, and it is a tricky path we tread, but doing nothing is not an option.
What the NYPD is doing is unconstitutional. I guess I'd go with the old saying better ten guilty go free than 1 innocent be punished. Probably not what you wanted to hear, but look at it this way. Muslims killed 3000 people in a country of 300,000,000 or 1/1000th of a percent. 6500 people die in the usa every day for one reason or another One day was 50% higher because of militant islamists. However, intrusive government under Pol Pot in Cambodia killed about 10% of the population. Stalin's policies killed an estimated 20,000,000 - 25,000,000. Hitler killed millions and not just Jews. Every one of these governments had no regard for the rights of their citizens.
Because it's better documented, look at the Nazis. They started ignoring the human rights of an unpopular religion and expanded to homosexuals, communists, and generally anyone who was known to disagree with Hitler's policies. Likewise the Soviet Union - anyone who was even suspected of thinking the wrong way was either killed outright or shipped off to Siberia to starve or freeze. I am FAR more concerned over the organized destruction of my rights by a government "not letting a good crisis go to waste," than by my possible risk of terrorist activities from a few hate filled fanatics. Government can't keep you safe (how many terrorists were stopped by the TSA? None - the airline passengers stomped Richard Reid and a couple of other headcases). But government can take away your rights and kill you.
Who do New Yorkers hate and fear the most? Gun owners. I can just see that dimunitive turd Bloomberg (with his taxpayer funded armed bodyguards to keep his worthless hide safe) getting up another task force to spy on American Rifleman subscribers, etc.
Let the muslims do what they will and arrest them after they have murdered thousands more?
The risk of this is the price we all have to pay for freedom.