Neither of those stories / movies actually attempted to show case the intelligent thought process of the main character. They did as I suggested and showed the view from out side. Neither show tried to depict how their thought pattern worked when solving any of the problems. Instead they showed them effectively turning in the result. They did it from the observers view.You don't need to be a genius to write about intelligent characters. IQ is also just one facet of intelligence. Intelligent or high IQ people can still make retarded decisions that screw everything. They can have character flaws like laziness, social, or emotional issues that hamper their success in whatever endeavor.
Still, what you are saying does have some truth to it. An absolutely basic writer that fails to contemplate or even recognize complex issues would have a hard time coming up with scenarios that actually display a character's intelligence. What's needed is not some "I have a high IQ, I am smart" writer, but basically just someone that doesn't suffer from Dunning-Kruger effect. At that point, a little bit of research can help with writing any type of character. Do you think the writers of Good Will Hunting or A Beautiful Mind, were anywhere near as intelligent as the characters they were writing about?
You didn't see internal dialog on the problem solving.
They also did a crap load of research again something I suggested above.
Seems your two examples tend to prove my point.
Intelligence is the ability to learn. There are no other facets to it. Mistakes are part of being human. That said smart people tend to have issues in other ways from less intelligent people.
A very smart person may fail to teach the basics of something for expects everyone to know it. They also fail to see the world from the less intelligent person's view point. They get over focused on issues and number of other flaws.
The lower intelligent person simply fails because they don't know how to proceed or can't grasp the larger picture.
I've seen scientist run their bicycles into the fence at LLNL because they were focused on the project they were working on rather than paying attention to were they are headed. They often worry to much about making a mistake thus fail to complete something like a test on time. Think of it like OCD.
The more someone knows the more they tend to realize how little they know in the grand scheme of things. People with little knowledge and intelligence have nothing to really base their lack of knowledge against which is why they can end up thinking they are smart. If I remember correctly Dunning Kruger is more about delusional superiority or over estimation of their own skill level vs others. I tend to think there are plenty of smart people that over estimate their skills and other things. They just are better at covering it up.
You are right on one aspect they have flaws. Often times the really smart person isn't the person producing the most results. Most the time it is some guy just smart enough to understand the issues who simply keeps plodding away at them.
IQ doesn't determine worth either. We all have different talents. Rather than getting hung up on what we can't do or trying to do stuff we can't do we should focus on the things we can do.