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From various sources who saw the 20-minute preview. Each quote should link to the relevant review:
First, there's a big secret full of awesome:
"We also learned a plot point that makes the film 400% more awesome, but Gareth swore us all to secrecy"
It's about a monster:
"It's noted in the report that Gareth Edwards asked them not to leak specific details about the monsters in the movie"
It's in the HALO jump scene in San Francisco:
Theyshowed the “skydiving” scene from the trailer, with something huge added in. Edwards said, “When you want to watch a movie with a kaiju like Godzilla, you don’t just want to see it fighting humans.”
We've been led to believe it's Godzilla, but it's not:
Lastly, I got an extended look at the HALO jump from the first trailer. It was every bit as dramatic as the promo would lead you to believe. You’ve seen a good portion of this.... once the jumpers get lower to the surface of a burning San Francisco, they don’t see exactly what the teaser trailer suggests…
So, exactly what else looks kind of like Godzilla, but doesn't quite match? Is it this?

I think the MUTOs might just be the warmup for the final act: a big Godzilla vs. "Godzilla" fight. Please someone convince me that I'm reading these facts wrong.