1. they set a pattern where they were killing a person a day + they were using the same car.
2. he constantly taunted the police, made calls, left them notes, left them cards. Shouldn't be that hard to use forensics to find out who it was.
3. he was actually connected to one of the victims. a truly random no-connections sniper would have been much harder to catch.
And yes people stopped running after he was caught...but that's because they knew the guy was caught. If it's a "terrorist organization", getting a few terrorists wouldn't solve anything, since you'd never know if there were more lurking waiting a few days till the next killing.