Too much lash may not be significantly noisier than the correct setting (click-click-click is normal for solid lifters), but it's not good for the bits and increases wear.
Not enough lash only has a single evil consequence: if, when the engine has reached the high end of its temperature range (long pull in high gear) any valve does not close completely that cylinder stops working. As HRL said, the exhaust is more prone to "tighten up" because of its higher operating temperature.