How much science needs to be in your sci-fi depends on YOU.
What "type" of sci-fi do you want to write? What are you ok with being known for? If you want to be known as a "hard sci-fi" writer, you HAVE to do the thinking legwork. Because if you don't, and you still try to call yourself hard sci-fi, someone with multiple degrees in those science will point out your writing doesn't fly and contains errors. There are people out there that are bent out of shape by logic holes in the new Star Trek films, and Star Trek isn't really hard sci-fi. Being credible in your logic is the bread and butter of some disciplines, and people learned in those disciplines WILL call you out on bullshit if you portray yourself as writing hard sci-fi.
On the other hand, if you never claim to be writing hard sci-fi, then you can get away with more. I would say...think of your favorite sci-fi authors. If someone told you you wrote like them, would you be happy? If so, see what they do in terms of believably and how much science is actually shown, and go from there. I'm a fan of Anne McCaffrey, but she has logic and science holes like whoa. So I aim to do better on the consistency and science front, while still trying to be engaging on the idea and character fronts, like she was.
Also...I'm somewhat on the side of not minding technical explanations of things in stories, if they are not over long, are grounded in real world science, and interesting. I *like* being taught in my books, and I think we've lost something by pushing "oh, people don't like details, explanations, or science!" at this generation of writers. Sure, it takes skill to pull it off...but I genuinely think not any more skill than it takes to write a good story. Then again, I set the standard for "good story" high, and feel by the time you're telling a good story, you should already have the skills to put a bit of science in the story without disrupting it.
