On a number of occasions I've been surprised to hear atheists argue that the Law of Non-Contradiction (LNC) has been shown by Quantum Physics to not be an absolute law - it has exceptions they argue. This is being consistent with their denial of God, in which a universe of absolute laws cannot be accounted for. This is an interesting reversal of what Christians are usually accused of - being illogical - as here it is the atheists that are appealing to illogical things being possible. The thing is though that the supposed contradictions have not be observed at the same time and in the same way - therefore they haven't broken the LNC at all. http://creation.com/god-particle-wave-duality
This article below discusses how more and more scientists are abandoning the idea of absolute laws in the universe - because to acknowledge them requires accounting for their existence - which cannot be done without a transcendent Law giver (God). http://creation.com/a-new-age-of-quantum-madness. A good example of a scientist who mixes science and weird mysticism is Rupert Sheldrake (See is 'banned' TED video here).
This is also well worth the read - http://creation.com/creationists-quantum-mechanics. It explains the difference between Quantum Mechanics (Quantum Physics) and interpretations of it - which is where the problem lies when it comes to the weird mystical ideas where human observers supposedly are influencing physical reality just by observing it, or having cats both alive and dead at the same time in contradiction to the LNC. These things haven't been observed at all - just theorised or wrongly interpreted from the actual experiments.
Yet another good article here - http://www.uncommondescent.com/hasnt-quantum-theory-proved-that-the-law-of-non-contradiction-that-id-thinkers-use-is-outdated/. In this article note the comment section which sums up the whole issue:
"Is that not a case of a thing being A and NOT A at the same time? [Superposition of electron spin]