Invalid Argument vs. Contradiction? I'm confused about the differences between valid/invalid arguments and contradictions/tautologies.
An argument is valid when the statement "all of it's hypothesis are true implies the conclusion" is a tautology.  
When we show an argument is invalid we are showing the above quoted implication-statement is false in at least one case.  Right?
Do we ever need to prove that an argument is equivalent to a contradiction?  I am trying to think of an example where this would be the case, or even could be the case, but...

Well, put model theoretically "valid" says that every model of your premises is also a model of your conclusion. "Invalid" says that there is at least one model of your premises in which the conclusion doesn't hold.
The only sense I can assign to "an argument being equivalent to a contradiction" is an argument in which the conclusion is a contradictory statement. In which case validity is still a live question and it breaks down into which of two cases we have: You can have contradictory premises, in which case the implication will be vacuously valid (since there is no model in which a contradiction is true). Or you can have a consistent set of premises, in which case the argument is invalid since there will be a model of your premises and none will be models of the conclusion.
The instances where either side of the implication is consistent are probably the usual ones you have in mind, like "if $x$ is a group then $x$ is abelian" or "ZF implies the existence of $X^Y$ for all sets $X,Y$".
 But in either case we can see that "valid" and "invalid" exhaust the semantic relations between premises and conclusions.
