First example: A half-dragon astral deva. Astral devas normally have wings, but they’re Medium, and the Half-Dragon template states that Medium half-dragons don’t have wings. Does the Astral deva lose its wings due to the template?
Second example: A half-dragon solar. Solars have a land speed of 50 ft., and a fly speed of 150 ft. The Half-Dragon template states that a creature of this size can fly at twice its base land speed, with a maximum of 120 ft. Does the solar have its fly speed reduced to double its land speed (100 ft.), or to the Half-Dragon template’s maximum fly speed (120 ft.), or does it keep its base fly speed (150 ft.)? Similarly, what (if anything) happens to its maneuverability?
Third example, based on the maneuverability part of the previous point: a half-dragon great wyrm (or any creature with a fly speed greater than 120 ft. but worse than the average maneuverability given by the Half-Dragon template). Does it keep the best aspects of its flight sources, or the worst aspects, or does it take one source for its wings in its entirety?