Every story has a setting in both space and time. It can be the past, the present, or the future. It can even be a mixture if you want to tackle the horrors of time-travel paradoxes. But even without those there are traps that arise.
Let's start with the future. (Cue Leonard Cohen: "I've seen the future, and baby it is murder!"). There is a movie called I, Robot (2004) based on Isaac Asimov's story of the same name. The very opening of it sets the place and time as "Chicago 2035". When the movie was made that was 31 years into the future, and it still seemed rather improbable that the future would be like that. Now 2035 is only nine years away and it's absolutely certain that version of reality will not exist by then. My advice for writing any futuristic story is to set it at least 1,000 years ahead. That way when the time comes you won't have to listen to people laughing at you and saying "sure got that wrong, eh?"
The present has its own traps, and they are often legal ones. Any reference to a politician or celebrity that might be construed as being based on a real person leaves you open to lawsuits. That even with the standard "Any resemblance between the characters and actual persons, either living or dead, is purely coincidental" disclaimer. And don't you want to change the last bit to "is truly unfortunate"? I know I do. Nevertheless, if there's enough similarity the disclaimer can fail in court. Then there are those who will claim you stole their work. It happens. Both the claiming and the actual theft. What people seem to forget is that we are all of a common culture, thus everything that goes into inspiring and creating a story is common to us all; it is only natural that two people would get extremely similar ideas for a tale without there being any contact between the two whatsoever. That's usually what courts demand for proof: substantial similarity to an existing (even if unpublished) work and evidence that the accused had reasonable access to it. That last part is why such cases typically fail. BTW, in the music industry this problem is a recurring nightmare.
The trap of setting your story in the past is somewhat of a paradox: you can never be historically accurate because history itself is not historically accurate. The seriously annoying deliberate re-writing of known facts aside, we do tend to uncover new evidence of old events from time to time and have to update our accounts of them. Imagine the joy of finding yet another city of Troy beneath the previous ruins (I think they are up to 14 distinct levels now). Of course even if your best research efforts allow you to write with unquestionable accuracy someone will still say "no, that's wrong. It wasn't like that". They then will go on to provide no proof of their claim, but once the lie is out there it will gain followers.
So what is the solution to all this? Lack of specific details. Carefully crafted vagueness that leaves enough room for doubt so that no one can say absolutely what you're writing about. Seems a terrible way to tell a story, eh? Yes, it is. For some reason the world is full of pendants who think every bard's tale is a historical document, even if they aren't Thermians (Galaxy Quest (1999)).
Although telling certain people "It's just a story" might not be a bad idea.
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