Honestly its more "real" than people think. Yes, its entertainment, don't let the science get in the way of the story. But for the most part, with exceptions given to things like using a Transporter to reverse the aging process, (again don't let the scientific theory of how it should work get in the way of the story), the science stays somewhat consistent.
The amount of power used by a Star Trek ship for example, it should be a lot, and a lot of times you only ever hear of the M/AM reactor as powering the whole ship, even in the episodes its said that that's the case. Well it's not. Everyone forgets that the Impulse Engines are powered by a separate system, a Fusion Plant, and I speculate that there would be one for each Engine (or more) so a ship like the Ent-D would have 3 to 6 Fusion Plants backing up the M/AM reactor. They mention it in passing in several places, but its never focused on. The one that comes to mind is Enterprise when they are tying in the new Phase Cannons, instead of tying their power connections to the M/AM reactor, they choose the Impulse Engines instead. Phase Cannons and their successor the Phasers are powered by Impulse Engines for the next 120 years, until the TMP refit ties the Phasers into the M/AM reactor.
A lot of the base science stuff. Tricorders, Sensors, Engines, and even shields, cloaks and transporters, are sound theories, they may not come to fruition as they were imagined to be 50 years ago, some may never come to fruition, but there's two generations of scientists and engineers that grew up on this stuff, and are testing those theories. As Corbomite said, almost all the computer technology that was in Star Trek and its spinoffs, we already have it. We have voice activated computers, we have Tablets, we have Cell Phones and Bluetooth devices to connect to the computers. Heck we've even got holograms.
I think a lot times we focus on the exceptions, the self replicating minefield, because the exception was needed to advance the story. But after the exception was used to advance the story, it was promptly forgotten about, because it really never could do that.