I'm watching Bones right now, and they casually use things I will bet good internet money do not exist, even at the design stage as a matter of fact to solve murders. But it's a standard procedural. Person of Interest knows where its science is buttered, and knows the AI "what if"s they ask are at the core of more than a few science fiction story.
On the flip side, when filming Leverage John Rogers countered "You can't do that! That doesn't exist!" with "I have one on my desk. You guys don't know what we can do."
Do you guys have examples of shows that don't call themselves AI, but use improbable tech all the time, and of shows that use real tech that just looks fucking impressive to use plebes?