I love Star Trek. Especially the original...the dynamic between Kirk, Spock and McCoy is far better than any modern bromance. (And I kinda hate that word).
Star Trek also predicted some aspects of the future beautifully.
I carry a PADD in my pocket these days and I suspect most of the people reading this blog too...we don't call them that, we call them 'smartphones', but they are the same thing. And, of course, there was a period when most cell phones looked exactly like Kirk's communicator.
Uhura's fancy earpiece? You might have one of those too, as part of a hands-free kit. We don't quite have tricorders, yet, but we're getting there. Videoconferencing didn't really exist when Star Trek was made.
And while hyposprays aren't in every doctor's office yet, they certainly exist and are in use.
So, what did Star Trek get wrong?
Everything. The original series was set in the 23rd century.
Look at what we already have now. Star Trek made fantastic predictions, but with the exception of the transporters and the warp drive (both of which were essential plot devices), they lowballed everything. We already have most of what they had on the Enterprise, in some cases better.
So, why aren't we going to the stars? Good question...perhaps we need somebody to invent the warp drive for us. Last I heard, Stephen Hawking was working on the math.