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Source: https://writers.stackexchange.com/a/37833
License name: CC BY-SA 3.0
License URL: https://creativecommons.org/licenses/by-sa/3.0/

Even in a world where, in theory, everything can be known, measured and recorded, there are still plenty of gaps in knowledge. This has very little to do with the actual tech and much more to do with the resources available. Even in an extremely advanced society, certain resources are still limited. The most important of these for generating mystery are time, people and ownership.

Time is probably the easiest. It's mostly related to more personal mysteries rather than (for example) a suddenly missing skyscraper but even there it applies. You could certainly have the tech to solve a missing person or someone's stolen datacore. However, that takes time. A lot of time, usually to the point where it's infeasible to cover 100% of all bases.  
You might imagine that total surveillance would help you catch every criminal all the time. In the best case scenario, you might have indestructible small drones, one for each person, that follows them 100% of the time. Congrats, you now have 12 billion (give or take) hours of footage to sift through every hour. Good luck finding the one minute of footage that shows you what happened. Data transfer speeds might make this even more of an issue and form a compelling reason for an investigator to hoof it to different datacenters and have some drama on the way to the mystery.  
Even DNA tests, if they were 100% foolproof, take time to complete. Sifting through the rubble remaining when a building vanished takes time. Traveling halfway across the globe to talk to a potential witness who got on the first suborbital takes time. And if the mystery is urgent, there's your drama.

The second is people. Your tech might be able to 100% scan and map out the physical world but people lie. And ferreting out those lies is a compelling source of drama on its own. But that's not all people do. People are envious, greedy and self-centered. Just because you _think_ you have the best tech on the block doesn't mean a different corporation or research entity hasn't developed something better and kept it to themselves. And why wouldn't they keep it to themselves? Hell, this doesn't even have to be tech. It could be someone lying about where they were the night before (at the club, cheating on their wife/husband/robot), someone inventing an elaborate cover story to avoid culpability or so they don't have to face facts (9/11 conspiracy theories come to mind) or any number of reasons.  
Third is ownership. Every technological development is impossible, right until someone cracks it and then it's only impossible for those who don't have access to it. As a good example, consider the invention of radar in WWII. The nazis had no idea why the Brits were so good at fighting them at night and the British intelligence service got remarkably creative with inventing reasons as to why their pilots could figure out where enemy bombers were in the pitch dark. Information and technological asymmetry is a great source of drama.

Original score: 3