Armin's Colossal Titan has no ears because he does not want to hear the screams of dying people.
Ymir takes her name from a legendary figure known as the first Titan shifter. This name comes from a creature known in Norse mythology as the 'Father of All Giants' and foreshadows Ymir's transformation into a Titan in Season 2.
The surname of the series' protagonist Eren Jaeger (or Jäger) means 'Hunter' in English.
In the 3rd episode of Season 1, Eren hits his head on the ground. He later appears with a bandage on his head and seems to have steam coming from it; this gives a hint several episodes before his Titan abilities fully emerge.
Bertholdt's way of sleeping with his feet up is a reference to the Hanged Man in Tarot, because the card's position represents the punishment of traitors, and thus foreshadows his betrayal alongside Reiner in the second season.
In Season 1, Commander Erwin, in his speech to the Survey Corps' 10 new members, says that 30% of them will die; in this way it is implied that 3 members will die: Bertholdt, Ymir and Sasha.
When Zeke and Eren meet in Marley, both of their shadows are seen to be headless; this indicates that they will be killed by having their heads cut off by Levi and Mikasa Ackerman in the final episode.
In the first opening song 'Guren no Yumiya', there is a hidden German line meaning 'Will you eat? No, we are hunters!' This was written specifically to establish the series' defiant tone.