Are There Limitations to the Proven Accuracy of GR and SR?

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Is it possible for parts of GR and SR to be wrong even thought there are things about them that seem to be undeniable?
 
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Sure. All measurements have limited precision, and the precision is continuously being refined. Also, we have limitations on energy levels that we can detect, both upper and lower limits. Beyond any of these limitations could lurk experimental facts which contradict relativity.

However, that won't save future generations from having to learn Einstein, any more than current generations can avoid learning Newton.
 
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