In fact, I do know of one experiment that contradicted string theory (as well as most modern theories candidates for a Theory of Everything):
http://www.nature.com/nsu/030324/030324-13.html
The article (as can be seen from the URL) was published in Nature magazine, a highly respected journal. Despite some searching on Google, I haven't been able to find out what the response has been to this experiment among theorists. Strangely enough, I can't even find references to the study in later science articles.
I think that what mghtymoop wants to say is that neither self-consistency nor consistency with well-established facts is enough to demonstrate a theory's correctness. For example, Newtonian Mechanics is mathematically self-consistent, but around the turn of the 20th century, experimental results were found which contradicted the theory. It might be possible to formulate multiple (and mutually opposing) mathematically consistent Theories of Everything that agree (empirically) with both Relativity and Quantum Mechanics. You claim that string theory is the only such theory at this time, but how do we know that, in the future, someone cannot formulate another theory that also fits this criteria?
I've read before that the "real" test of a scientific theory is its ability to correctly predict experimental results AFTER the theory is published. Thus, it would be good (and arguably necessary) science to doubt the correctness of the Theory of Relativity in say, 1917, before conclusive evidence for it was obtained. We accept the theory only after many independent experiments confirm its predictions.
Remember, there are many theories in the history of science that seemed plausible when they were first proposed, but were later falsified. For obvious reasons, they aren't taught very often.