What physicists call a theory is basically what laymen call a fact; it's a hypothesis that people have tested empirically over and over again, without falsifying it. Quantum mechanics is one of the most tested theories we've got, so if that's not "established fact", I'm not sure what is. It's true that quantum mechanics and general relativity aren't really compatible, so physics is not "complete" yet; but quantum mechanics does accurately describe systems where gravitation is irrelevant.
If you're still doubting that quantum mechanics can have real-world applications, here are some inventions that were based on quantum mechanics, from the top of my head: lasers, transistors and scanning tunneling microscopes. In addition, many other phenomena (chemistry, radioactive decay, degeneracy pressure, photoelectric effect, etc.) weren't really understood before quantum mechanics.
Source: http://rss.slashdot.org/~r/Slashdot/slashdotScience/~3/akhW918R2MQ/story01.htm
Ryder Cup 2012
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