How dumb is the client really?

[Skandranon]

Not an answer to your question, but in some cases it CAN and WILL overrule the server. 
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One of the cases where this is actually having significant effect on normal players is the fact that the client determines the falling damage you take when you jump from a height into water. If your client is late to load water, as many clients are, it will determine your fall as if the water wasn't there - as if you jumped directly into the floor - and apply falling damage accordingly (probably killing you).