After Briareos' weapon is sliced into pieces, he throws the weapon to the ground in one piece.
When Deunan follows Briareos into the locker room all of the locker doors are closed. After Briareos exits, she roundhouse kicks a now open locker door.
In the arm of Briareos there is a Tatoo written in Greek which directly transliterated would be "godsito erdso sum". Correctly would be "cogito ergo sum", but that sentence is not greek but latin/french (je pense donc je suis), and his author is Descartes.
In the beginning of the movie, the bible is quoted. They use "Revelations 12:4" The book is actually called "Revelation" (no s at the end)
When Deunan is trying to save Briareos from falling off of Mobile Fortress 7, she is using one hand to hold onto him and is repeatedly shown reaching out with her remaining hand to attempt to input the password.
When General Uranus is on the roof trying to convince Deunan and Briareos to give him the Appleseed pendant, it is raining heavily, but everyone's hair is dry and blowing around in the wind.
When Briareos' weapon is sliced into pieces, the places where the gun is cut can be seen before the cuts are made.