Stupidity: Steve Trevor is the leader of a group of Allied spies, and they are traveling with a gorgeous woman who has shown to have amazing fighting skills and super powers, but they allow a group photo to be taken with Diana in her armor. They don't know who is taking the photograph nor what they intend to do with it. Their photograph circulating through a news publication or passed on to an enemy's intelligence service could compromise himself and the rest of his team, and they would absolutely know that. Undercover agents do not pose for photographs.
Character mistake: Chief says the poison gas should be flammable because it's hydrogen-based. Hydrogen is the most common element in the universe, and there are plenty of non-flammable substances that contain hydrogen - the most notable of which being water.
Plot hole: How is it possible that Diana is unaware of the concept of marriage? She has a grasp of multiple languages and cultures and can recite Socrates. Socrates often spoke of marriage, so even if her people do not marry, it makes no sense that she is completely unfamiliar with this human custom.