Deliberate mistake: The Messerschmitts have painted yellow fronts, this wasn't done by the Germans until after Dunkirk. Christopher Nolan has admitted doing this deliberately so the audience could tell the difference between the Spitfire and the Messerschmitt during the combat scenes.
Continuity mistake: As the lone Spitfire trails and attacks the German bomber, he hits the right engine, which starts smoking but the trail quickly fades. He then hits the left, which smokes a lot. We then see the same attack from below, and from this angle the both engines are smoking equally badly.
Answer: That's exactly how it was. If you search for images of the evacuation, the troops were stood in lines, waiting to be evacuated. The Germans were held at bay, and the air raids were periodic, so there was little risk on the beaches.