As you've already mentioned in another hint, there are extra points that can be acquired by breaking pots, barrels, skulls and the like. However, pay close attention as you break these objects, as sometimes Orange Crystals lurk within. These will reward you with extra points, in the range of 200-800 points per crystal.

Correction by Colin Moriarty: If you shoot a jar or other object and a gold coin comes out, shoot the gold coin immediately. They're worth 1,000 points if shot immediately, and as the coin floats down, it becomes worth less and less, until it's worth next-to-nothing.