The first is a dark, ghostly figure, which shows up after Kratos's first battle with two smaller enemies. As he and his son walk through some arches, you can see the figure on the right hand side, just as it zooms off the screen to the right. You can see it for yourself in the gameplay demo at around 3:45 or in the GIF below.
The last spotting is a big one. As Kratos and his son look across the Scandinavian landscape, you might notice there's an icy river flowing in the valley below. However, as NeoGAF user Fliesen points out, it's not a river.
"Nah, man, those are scales," they wrote. "And they're clearly moving in front of the treeline--if that were a river, you'd see some kind of shoreline."
Some users believe it points to an "epic" boss fight with the World Serpent, Jörmungandr. Its "World Serpent" moniker comes from the fact that it grew to be so big that it could stretch itself around the world and touch its own tail. The thing in the gameplay demo, which can be seen around 9:15, looks pretty big. You can see it for yourself in a GIF below.
We recently got the opportunity to talk to game director Cory Barlog, who talked about the challenge of making people take Kratos seriously.
Barlog also joined us on GameSpot's live E3 stage show, where he discussed reinventing Kratos and the series' perspective. Additionally, he explained how Kratos could be in the midst of Norse mythology, after spending so much time in Greece's mythos.