Continuity mistake: When you first meet the Doom Dragon on top of the Mars Lighthouse, its red head is on the left. When you actually battle the Doom Dragon, its red head is on the right. You see it both times from the front, so it's not an angle issue.
In the Mars Lighthouse, in the same room you defeat the Flame Dragons in, return after you have defeated the Flame Dragons and fire off the cannon. A crack will appear where the ice was, even though there is no ice.