Yeah, nice trap, isn't it?
That stories could become dated is an interesting point: I've read almost everything written by H. P. Lovecraft, and although he wrote in the 1920's and '30's, his narrations are still modern (in a positive way!) Of coures, when it comes to technical descriptions, you can tell that they are around 80 years old. And often he used exact dates. But there's something about his work that makes it timeless. Is it the contense, the style? A little bit of both.
Using brands to create a feeling of a certain epoch, as mentioned by many of you, is not only a good method, it's more or less necessary. Can you imagine the '90's without Swatch? Or the '50's (-'77) without Elvis? He's a brand, too.
But a story which isn't designed to take place in the '80's and therefore doesn't use the narrative possibilities for style, historical context etc., should be dissociated from temporary trends.