Ribosomal Turing Machines, DNA/RNA computation
I'm no expert at this but I don't think you need a Turing machine to achieve this, at least for DNA, since in conventional sense (not including carcinogenic factors such as UV) the most probable stage in which a DNA mutation can happen is during DNA replication so DNA polymerase engages in proofread to ensure accurate DNA replication, and then the DNA can get back into being heterochromatic (eventually). This will be more difficult for RNA as they are single stranded although they do fold onto themselves.

Also there many many strands of RNA that are produced through alternative splicing, VDJ recombination and RAG imprecise rearrangements for antibody production, which can give rise to infinite possible RNA productions. So how would you know what is "good" and what is "bad" in terms of RNA and its production. Half the time we don't even know what they do and what their roles are and the only reason we call something as a "bad" or "faulty" RNA is because it is having a negative effect not because we understand the precise role of the sequence, which means a theoretical table would be useless.

So in short, a turing style protein machinery is neither possible (due to almost infinite potential number of RNA produced) nor feasible (since the number of proteins that would have to check each RNA sequence would in turn have to be almost infinite). And none of these takes into account SNPs i.e. individual variations, which can produce proteins with different sequence but identical structure/function, since obviously any lethal variations would be selected against but thats a whole different argument.