Rip, I'd like to take a stab at this.
The criteria for reasonable searches is traditionally linked with the concept of 'probable cause'. A police officer may search a person who they have probable cause to believe is committing a crime. For example, if the person is stopped right after a bank robbery has taken place in a car that matches description, and the right side of the person is covered with dye, then there's probable cause to believe that this is the person who has committed the crime.
The problem with the subway searches is that the presumption of guilt is in effect. Random people are being searched without probable cause being established. If, on the other hand, they searched people who were being surveilled because of suspected terrorism links, that might be different, but the stated actions by the police is that they are deliberately searching people who are not suspected of anything.
That meets the criteria of 'unreasonable search'.