The proof against local realism is humankind’s the most relevant finding in the realm of science and philosophy; there is no excuse to be ignorant about it while pretending to be interested and knowledgeable about cool science and its implications for philosophy. It was a difficult topic once, but from now on, there is no excuse anymore: Any good high school student, certainly any university undergraduate is able to follow the arguments as long as there is no religious/obsessive hurdle to overcome internally.
Here is a study guide to the disproof of 'local realism' and the solution of the Einstein Podolsky Rosen paradox. UPDATE: What is written in this post is now mostly much better accessed in this, extremely pedagogically written article: http://arxiv.org/abs/1311.5419
The following posts help to understand the preprints:
1) Disproving Local Realism and Hidden Variable Madness. The experimental setup is introduced and the ground set: Quantum physics disproves local realistic models. It may be helpful to also read about the Quantum Randi Challenge, which will make it yet clearer that no locally realistic model can be quantum mechanical. However, the Quantum Randi Challenge is a side issue here.
2) Spooky World or Crazy Mind: Nonlocality versus Antirealism is somewhat of an introduction that should help to understand that there are two sides to local realism, namely (Einstein) locality and (direct/naive) realism. This post may help to understand the introduction and thus the general problematic, but it is not necessary to understand the main arguments.
3) A classical model is introduced in Many Worlds by Splitting a Wiener Sausage. That model is simplified further in Many World Sausage with Correct Quantum Factors. The latter article shows that the model is able to come up with desired factors needed in a quantum model (UPDATE: Such models have now also been found).
4) Classical Parallel Worlds and Local Non-Locality yet again clarifies that although the correct factors may be found in the initial sausage model, the model is still classical.
5) Gambling in the Multiverse: Empirical Probability versus Classical Fair Meta-Randomness explains the difference between classical probability and quantum probability and why the probability that we empirically see in experiments is the quantum probability. This post contains a tree that was too off-topic for the preprint article yet it should be very helpful to most readers!
6) Einstein Podolsky Rosen Paradox Resolved by Local Modal Realism finally explains how the sausage model is turned into a quantum model. It introduces the growing branches instead of cutting the sausage and discusses the crucial step that turns the direct realism into a modal realism.
7) Why Einstein Could Not Solve EPR Though He Could Have explains that modal relativity is a necessary paradigm that was already indicated by special relativity.
 S. Vongehr: "Many Worlds Model resolving the Einstein Podolsky Rosen paradox via a Direct Realism to Modal Realism Transition that preserves Einstein Locality." arXiv:1108.1674v1 [quant-ph] (2011). UPDATE: This reference is the first paper on the possibility of such models, but they have now actually been constructed and are much better explained in S. Vongehr: “Against Absolute Actualization: Three "Non-Localities" and Failure of Model-External Randomness made easy with Many-Worlds Models including Stronger Bell-Violation and Correct QM Probability” http://arxiv.org/abs/1311.5419 (2013)