I've heard that breaking the wrong type of block with a tool, e.g. sand with a pickaxe, uses up twice as much durability as breaking the correct type. Is this true?
Breaking sand with a pickaxe will damage the tool one point (using up one point of durability), the same as breaking any other type of block.
This goes for axes, pickaxes and shovels, you can break any type of block with them and incur no penalty.
The only case where double damage is done to a tool is when using a sword to break blocks, or using a tool to hit mobs. Hitting a mob with a tool will cause two damage to the tool per hit, breaking a block with a sword causes two damage to the sword.
The exception to this is blocks which break instantly, like torches, beds, paintings, redstone etc. These cause no damage to any tools, or swords.