I believe the thing to keep in mind is that Law Enforcement isn't as smart or as organized as they would have you believe on TV.
Most Law Enforcement in the U.S. use these "new powers" to spy on their spouses, girlfriends, ex's, friends, family, etc... No one is monitoring them and the few who get caught just gets a slap on the wrist and told not to do it anymore.
They really don't have to monitor your pc or anything else if they decide they want to set you up as an example. Just like when they pull you over and "find" drugs which are not yours. They can also plant files on your hard drive to "prove" whatever they want to prove.
Even if you have proof that these are newly created files they simply have the prosecuting attorney either not allow it into evidence or not mention it to the jury. So you're still screwed.
If all else fails one of the first thing they do when they "arrest" you is to announce to the public that you had porn on your computer so obviously that means that you're guilty of something. Never mind that THEY have several hard drives filled with porn at home. In the U.S. the police immediate start a discredit campaign upon the arrest so that the public sees you as guilty before your court hearing.
About a year ago there was a case where the police had placed kiddie porn on the torrent type sites. When someone tried to watch the video it would send info back to the police so they could track who had been watching the video. UNFORTUNATELY, they caught someone who didn't have any porn on their computer. They had downloaded what they thought was a disney video only to discover it was the porn video when they played it. Evidently the police are not aware that people rename videos and other files.
Moral of the story is this: If they're out to get you -- they're going to get you. The only thing you can do is sit down, take a deep breath, place your head between your knees and kiss your ass goodbye.