Someone recommended it on here the other day, but D-Day by Stephen Ambrose is an extraordinary book. The complexity and magnitude of D-Day is overwhelming, but Ambrose did a great job of weaving it together into a book that's very hard to put down. I can't imagine being in that first wave at Omaha where the casualty rate was close to 100%.
The diversionary campaign (Operation Fortitude) was fascinating. We went to great lengths to make the Germans think the landing would be elsewhere, including using dummy aircraft and boats and German double agents, and it worked.
One of the key objectives for the paratroopers landing at midnight was to take a bridge called Pegasus bridge near Caen, I believe. The Americans had to take the bridge in order to move troops and supplies into France. The Americans took the bridge and a panzer division was nearby, in position to take it back, but never received orders, so like you said, they sat there. I think there was a similar story regarding the hidden guns at point du hoc (I think). As I said, his paranoia and his incistency to control everything led to his undoing.