What am I talking about? The list is huge, but I think we can focus on a few popular errors.
For example, a ship blows up in space. What do we see (and hear)? A fireball, a roar...maybe even some debris whooshing past. Of course, there's no sound in space, so that's an easy one. Less obvious is the fireball. Fire needs a fuel and oxidizer (usually oxygen). Since there's no oxygen in space, how can a flame go beyond the confines of the inside of a ship? It can't.
How about artificial gravity? Since our best understanding of gravity suggests it is a question of deformed space-time, objects "feel" each other by following the contours of the fabric of space-time. As far as we know, gravity does not behave like a magnetic force, so there is no way to shield it or create it. So much for theory, but let's suppose you CAN manipulate it and create artificial gravitational forces. How would you limit them to the flooring of a spaceship? I've seen astronauts leap out of ships directly into space without being pulled back by that artificial gravity. Pretty awesome invention.
The Enterprise shoots out a photon beam, aka, a laser weapon. And we see the beam. Any problems with that? Remember there's no air, no molecules for that beam to bump into and light up. We should not be able to see the beam. But how exciting would it be to see the target mysteriously explode? Without flames? Without sound?
Space travel - wow, this is a big one. How often do we see a ship traverse the galaxy? Our modest little Milky Way is about 100,000 light-years across. That means that even at the speed of light, it would take 100,000 years (Earth time) to get from one end to the other. Ok...there's Einstein and his theory of relativity, which means that time dilates as you approach the speed of light...so time for you passes more slowly and you just might live long enough to complete the trip. To make this as realistic as possible, if you accelerate at 1 G (equivalent to Earth's gravity), it would take you about a year (Earth time) to get to about 99% of the speed of light (you would need a year's worth of fuel!). You'd have to travel a bit longer than that to reach 99.99% the speed of light. At this point it would take you about 1100 years (your time) to cross our galaxy. Convenient space travel will require something akin to a wormhole or entirely new science (tachyons, warp drive). Be wary of wormholes - although they represent a theoretical way to span huge distances in an instant, they also promise to bring you to a different time (past or future).
So where's the fun? We want noises in space, we like to travel quickly, we want instant communications (not covered here), and we want all our alien friends to speak English. Suspension of belief is a great pleasure. The "what if" question can be replaced with "what the heck" and we'll all get a kick out of great SF stories, because those stories are actually about us more so than the methodical extension of known science. Having nodded to the fun factor, Science in Science Fiction can also be a poignant warning, a realistic vision of tomorrow, which gives the reader or viewer a sense of place and destiny.
I've included herein a short list of links to articles that may be of interest. Enjoy.
10 Myths About Space Travel That Make Science Fiction Better – Charlie Jane Anders
The Real Science of Science Fiction – Susan Stepney
Yes, It Matters If The Science In Your Science Fiction Story Is Accurate – Charlie Jane Anders
Putting the Science in Science Fiction – Tedd Roberts
Time Travel in fiction – Wikipedia
Technology in Science Fiction – Wikipedia
The Best Hard Science Fiction Books of all Time – MIT Technology Review
More fi than sci – Mukul Sharma – The Times of India
Don't Ruin Science Fiction with Science – Alex Reissig
Space Flight in Science Fiction: Getting off this Rock – Patty Jansen
How Interstellar Travel Works – Karl Tate
A Primer on Time Travel - Damon Shavers
The Biggest Errors in Hard Sci-Fi – Joseph Shoer