(at around 43 mins) The discussion in the boat about "the pleasures of the flesh" was improvised.
Steve's timepiece is a pocket watch, adapted with a leather case to be worn on the wrist. Pocket watches were the norm at the time (they were usually worn on a chain), but they proved to be impractical in front line action. Because timing was critical for coordinating large-scale action (such as the use of infantry maneuvers in conjunction with artillery barrages), soldiers began wearing timepieces on their wrists. This fashion spread to civilians after the war and adapted pocket watches into wristwatches, which became as the preferred fashion of timepieces in the 20th century.
The scenes of Themyscira were shot in Southern Italy, on the Amalfi Coast. Production designer Aline Bonetto said the location was perfect: "Italy had beautiful weather, a beautiful blue-green sea, not too much tide, not too much wave."
(at around 3 mins) Some of the Amazons have flesh colored cloth over one side of their chest, almost seeming like one breast was uncovered or nonexistent (this is very apparent in the opening sequence when young Diana watches the training and Antiope walks over to talk with an Amazon so clad). This may be a reference to the fact that Amazons are often depicted in art as having one breast exposed. Ancient sources even state that Amazons cut or burned off their breast on their dominant side so that it wouldn't interfere with combat, especially with a bow. Some ancient sources suggest that this is the source of their name; "a-mazos" in Greek means "without breast".
General Erich Ludendorff was a real person and he was ruthless, although not necessarily more so than any other high commander in any WWI nation. As supreme commander of the German forces, he authorized the use of mustard gas, a corrosive agent that could quite literally melt tissue, and that depending on the exposure would inflict temporary or permanent blindness, lasting damage to lungs and an extremely painful death. With the armistice, Ludendorff later supported Adolf Hitler's failed coup, but grew to dislike Hitler long before the Nazis actually took power.