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.
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.
Suggested correction: She has never seen a man either. She read about them, but never actually saw one. One might question why she doesn't understand a man if she read about them, and yet she doesn't. Same thing with marriage.
She had never seen a man, but she knew that they existed. She speaks multiple languages, despite never having met someone from any of those cultures. My point is, if she's so well versed in world cultures, how has she never heard of the concept of marriage?
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.
Suggested correction: Hydrogen is explosive in air at concentrations greater than about 4%.
Pure hydrogen is flammable, yes. However a chemical compound that contains hydrogen would not necessarily be explosive, or even flammable. As the original mistake stated, water contains hydrogen and is not flammable. Whilst other hydrogen-containing compounds are flammable (such as hydrocarbons), the presence of hydrogen alone is not the reason for its volatility.
Continuity mistake: When the picture of Diana and Steve and co. is taken in Veld, she is wearing her black cloak, but she left that and her other clothes in the trenches, on the other side of no man's land.
Suggested correction: She's in Flanders, in November, and the battle was over. It's cold, and probably worth going back to the first trench to get her cloak again, which they now have plenty of time for.
Except I seriously doubt it would still be here as poor, displaced people would likely have taken it to keep warm, like the woman and child she spoke with.
Suggested correction: The photographer is not a reporter, he is one of the villagers. The photo was not taken to be circulated through print media, it was taken by the villagers to commemorate the day they were liberated. There only appears to be one copy of the photograph (which Bruce Wayne finds and sends to Diana), so the likelihood of it falling into the German's hands is incredibly slim.
BaconIsMyBFF
It does not matter who took the photograph or why, or what he chooses to do with it. Undercover agents do not pose for photographs.