The real answer here is to profile, and concentrate on the likely bombers: 20-35 year old ME males. 90% of the searches should involve them. The rest SHOULD be random, to prevent them from being confident they can get by with a ringer.
We have limited resources, and MUST concentrate or forces while keeping the enemy off balance. Anything else is doomed to fail, and frankly madness.
Should this include any place where people crowd together, including open markets?
Just to put things in perspective, the chances of dying in a terrorist attack of this nature are minuscule, considerably less than the chances of dying in a traffic accident. Subjecting people to searches only makes them more nervous and edgy, and that gives encouragement to the terrorists.
Keep in mind that Britain has a more extensive surveillance apparatus than we do, and it doesn't seem to have helped them. That's because they allow Islamic extremists of every stripe into their country. A better policy for us is to just find the terrorists and kill them, and in the meantime, make sure we keep out aliens who pose any kind of security risk.