Family-Unfriendly Aesop: Quite a few aesops that are typically shown as being negative as spun to give a positive twist. Such as envy, Fudou says that envy can either make someone attempt play dirty or use it as a huge motivator. Cue Sirius, using his envy for fuel along with the other two pilots, and spins his Aquarion around to make a monster of a storm and defeat the monster of the day.
Freud Was Right: One episode has Pierre show "addiction" to combining (yes, really). To cope, he takes a cup and a cup holder and repeatedly inserts the cup into the cup holder. He is also seen in that episode doing similar motions with a pen and its cap.
And to add to the double entendre, he spends his entire class staring at his female classmates (never the males). Granted, he is the Handsome Lech, but it is strongly suggested that this extreme is due to the addiction.
Moral Event Horizon: Touma killing Baron in Episode 13 and the army scientists killing Futaba then using his feathers to create superhuman killing machines.
With regards to the second one, it is treated as one, but considering that not only was it a viable way to end the war and save the human race from extinction, but also according to one of the overheard scientists, Glen volunteered for it, it might just be reasonable. When your enemy is indiscriminately taking humans for food, killing one of theirs to make weapons to survive doesn't really register on the Bad-o-Meter.
Also, it doesn't help that afterward Sirius spitefully stated that Futaba's life was worth far more than the people he killed, and we're apparently meant to agree with that.
Touma is really more of a Manipulative Bastard; he honestly thought of humans as we think of cattle. Plus Baron wouldn't have been killed had Apollo not grabbed the Schmuck BaitIdiot Ball and waited a few episodes.
One True Threesome: The ending with Toma, Apollonius, and part of Celion (i.e. Sirius) together forever inside Aquarion.