There is, in my mind, a big difference between a scientist publishing a paper in which they investigate some outlandish science-fiction-like concept (such as time travel or anti-gravity) and find evidence AGAINST it, and one where they find evidence FOR it.

The former is a reasonable result, and although expected the research provides evidence to support the hypothesis. The latter is an extraordinary result and wise scientific practice would require extraordinary evidence.

(It also helps if you don't get disavowed by your own co-author and by other labs you say confirmed your results.)

I see nothing wrong with publishing ordinary evidence for extraordinary things. I mean, I still wouldn't beleieve the extraordinary thing, but it could still be useful.

How about the hit to reputation? Many would level the criticism that publication was too early.

That's a problem that needs to be fixed.

As unlikely as these findings are, has anyone actually replicated the experiment?

Yeah, JPL, about 15 years ago. He measured something, and was conservative with the paper, but a journo got his hands on it from a leak at nature, the papers ran with "Flying cars!!!!", and the rest, like his reputation, is history.

There was a half hearted attempt http://pdf.aiaa.org/preview/2001/PV2001_3363.pdf

However, it wasn't an identical attempt in terms of materials, process, etc...so I'm not sure it really counts.

This might make for some interesting reading: http://arxiv.org/pdf/1312.0958.pdf

Is this what the technology in the movie "Primer" was based on?

No, primer is about time travel, not anti-gravity or gravity shielding.

Off the top of my head, I remember the engineers' initial idea was to reduce the weight of a load in a truck. Then, they realized the technology could be used to build a time machine.

Ah yes, the 'object inside' right. I'd totally forgotten about that, apologies.

Or in the process accidentally invent limited time travel and find that you have better things to do.

[1] http://www.imdb.com/title/tt0390384/